Many new viewers of Saved by the Bell are confused by the changing characters and various settings for Saved by the Bell. The astute soon figure out that there are some rather major continuity lapses between various parts of Saved by the Bell. The first major continuity lapse is easily understandable once one knows the history of the show itself.
Saved by the Bell did not begin its run as "Saved by the Bell", nor did (most of) its first season air on NBC.

The "Good Morning, Miss Bliss" Paradox:

Saved by the Bell first began as a pilot for NBC, and the name of the show was Good Morning, Miss Bliss (GMMB, for short). The GMMB pilot did air on NBC back in 1987 (it aired in The Facts of Life's timeslot). The pilot for GMMB did not have any of the cast of Saved by the Bell (or even any of the later cast of Good Morning, Miss Bliss). Instead, the pilot starred Hayley Mills, Brian Austin Green (of Beverly Hills, 90210 fame), and Jaleel White (of Family Matters fame)! In the pilot, "Miss" Bliss was actually a newlywed. And Green did not play Zack Morris, or a "Zack Morris-like" character; instead he played a character who who super serious, and who always wore business suits to school.
Still, NBC passed on the project (at this time), and The Disney Channel picked it up and filmed 13 episodes in 1988 for a winter 1988-spring 1989 run on The Disney Channel.
Indeed, Good Morning, Miss Bliss was originally conceived as a vehicle for Hayley Mills, a popular actress who had done many previous movies for Disney. Mills played the character of a widowed junior high school teacher, Miss Carrie Bliss, and the show was mostly about her experiences as a teacher (as well as her hapless love life). (The "Miss Bliss as a widow" storyline seems to be consistent with the pilot, and some of us believe that the GMMB episodes with Zack, et al. took place a year after the pilot episode.) This was the first incarnation of "Saved by the Bell".
The setting for the show was John F. Kennedy Junior High School in Indianapolis, Indiana. For the remainder of GMMB's run, Zack (Mark-Paul Gosselaar), Screech (Dustin Diamond), Lisa (Lark Voorhies) and Principal Richard Belding (Dennis Haskins) were the other main characters in the show. However, there were still other characters (e.g. Nikki, Mikey, Tina and Milo) in the show who were never in later seasons of the Saved by the Bell show. Also, the focus of GMMB was Miss Bliss first, and basically Zack Morris second.
The show was produced by Peter Engel, and William F. Phillips was the Executive in Charge of Production. After the move to NBC, some of the GMMB episodes were rerun on NBC in the summer after the Grade 9 season along with an introduction by Zack explaining that this was what happened to him "in junior high". In any case, it is the absence of Kelly and Jessie and Slater, and the setting of the school in Indianapolis that account for the most glaring continuity lapse of the Saved by the Bell series.
There were 13 episodes made of Good Morning, Miss Bliss, but Disney decided not to continue with the project. So it appears Producer Peter Engel, William F. Phillips, et al. took the show back to NBC which then decided to pick up the project again, as its first live action show for NBC's Saturday morning line up. Major changes were made for the show's second incarnation. First the name of the show was changed to Saved by the Bell (SbtB, or SbtB, tOS for short). The setting was changed from JFK, Junior High School in Indianapolis, IN to Bayside High School in Pacific Palisades, CA, which is southwest of Los Angeles and Santa Monica. The characters of Zack Morris, Screech Powers, Lisa Turtle and Principal Richard Belding were kept for the show, and three new main characters were added: Kelly Kapowski (Tiffani-Amber Thiessen), Jessie Spano (Elizabeth Berkley) and new transfer student, A.C. Slater (Mario Lopez). The other characters, including Miss Bliss, were dropped. And, of course, the focus of the show changed to Zack Morris, and to a lesser extent his friend Screech. Some of the original production crew of GMMB did not stay on for SbtB, though some other members of the crew continued on with the show as SbtB.
But this introduces the first continuity questions. How is it that three students and a principal can move 2000 miles between junior high and high school and still stay together in the same school? Why does Zack tell Slater in the first episode of Grade 9 that he's been after Kelly for the previous "2 years (and 6 boyfriends)" when no mention is made of her in GMMB? Why is no mention made of Zack's "good friends" from GMMB, Nikki and Mikey in SbtB; and why is no mention made of Zack's "friend since the first grade" Jessie in GMMB? Why is Zack's father's name Peter Morris in GMMB, and why is it Derek Morris in SbtB (and why do different actors play Peter and Derek)? Why is it said in GMMB that Zack's father and mother are divorced when they clearly are not divorced in SbtB? Why is mention made of Screech having a brother in GMMB, when it is clearly stated that he is an only child in SbtB? What is the explanation? The only explanation for this is that there is no good explanation (unless you want to count alternate realities). Saved by the Bell is a farce by nature, and its characters and gags were the main focus of the show. Unfortunately that means that the plot and the show's continuity must (and did) take a back seat to character development and to the comedy in the series, especially in its change from Good Morning, Miss Bliss on Disney, to Saved by the Bell on NBC.

A Short History of SbtB, the original series:

Saved by the Bell, the original series (SbtB, tOS for short), debuted on NBC on August 20, 1989 in primetime. Saved by the Bell aired twice in primetime (once on August 20, and once later) before settling into its Saturday morning timeslot starting on September 9, 1989. SbtB, tOS played out most of its existence within the reworked plot definitions mentioned above in NBC's Saturday morning line-up. For Grades 9 through 12 (1989-93), the show followed the adventures of Zack, Screech, Kelly, Slater, Jessie and Lisa in Bayside High, and in some other settings such as at the Mailbu Sands Beach Club, in Palm Springs and in Hawaii. For specifics on the episodes of GMMB or SbtB, see the Episode Guide at this site.
Also during the Grade 12 season of SbtB, tOS, the Saved by the Bell-Hawaiian Style TV movie was aired on November 27, 1992 in primetime on NBC. It was rerun again in primetime on August 31, 1993 on NBC in the run up to the primetime premiere of Saved by the Bell-the College Years (see below).
But something happened when Grade 12 rolled around. By this time, the show was very popular. But something needed to be done now that the show had reached the end of high school. The graduation episode had been filmed, and even a SbtB TV movie set in Hawaii had been filmed after that (though chronologically, it actually appears to be set in time after the Grade 11 season and before the Grade 12 season, and obviously it aired during the regular Grade 12 season). But the question was, what to do with the show now?
Another problem came when Tiffani-Amber Thiessen (Kelly) and Elizabeth Berkley (Jessie) decided that they wanted to move on and leave the show half-way through the Grade 12 season.

The "Tori/Kelly-Jessie" Paradox:

SbtB producer Peter Engel seems to have come up with several solutions. He appears to have decided to produce another partial season of SbtB proper in Grade 12 at Bayside, using a new female character in the place of Kelly and Jessie. This would allow them to finish the Grade 12 season of SbtB, tOS. This, in turn, would allow the producers to develop two new series for production: Saved by the Bell: The College Years, the continuation of the adventures of Zack and Screech (and Slater), and Saved by the Bell: The New Class, the continuation of the adventures of Mr. Belding and the students of Bayside High.
So, a new character was created for this "half" incarnation of "Saved by the Bell". The character's name was Tori (Leanna Creel). This introduces another continuity question: it is still Grade 12 at Bayside, so where are Kelly and Jessie? It is obvious that the "Tori" Grade 12 episodes are supposed to take place in the same time-frame as the "Kelly and Jessie" Grade 12 episodes; we know this beacuse the "Tori" Grade 12 episodes were aired concurrently (i.e. on the very same days) that "Kelly & Jessie" Grade 12 episodes were in the '92-'93 Grade 12 season on NBC. So what's going on? The way to explain away this apparent discontinuity is to say that the "Tori" episodes are taking place at the same time as the "Kelly and Jessie" episodes, but that Kelly and Jessie are "off screen". Thus, Kelly and Jessie, and Tori, must be "in different classes", and we, the viewer, are seeing Tori on different days and different nights or in different locations than when or where we saw Kelly and Jessie in their Grade 12 episodes. So why are Kelly and Jessie almost never mentioned in Tori episodes, and vice versa? And why is Lisa's hair style different in some of the "Tori" episodes from the hair style she had through the entire "Kelly & Jessie" Grade 12 year? Well, you got me! and this explanation only goes so far.
Though filmed before the "Tori" episodes, the Grade 12 Graduation episode was shown after the Tori episodes (as apparently was the Hawaii TV movie), in primetime on NBC on May 22, 1993, along with the pilot to Saved by the Bell: The College Years (see below). It was rerun, again with The College Years pilot, in the regular timeslot for the premiering Saved by the Bell-The College Years on Tuesday, September 7, 1993 at 8:00 pm EST.

The Resolution of SbtB, the original series:

At the end of SbtB, tOS, it looked like the gang would all end up at different colleges. But in the pilot of Saved by the Bell: The College Years (SbtB-tCY for short), we saw that Zack, Screech and Slater ended up going to "California University" in the San Francisco Bay Area (presumably in Berkeley). This was the third (and last) incarnation of Saved by the Bell proper. After the filming of the pilot, Tiffani-Amber Thiessen (Kelly) decided to rejoin the cast of SbtB-tCY, and was seen in the College Years for the rest of its run.
SbtB-tCY ran 18 episodes (and a pilot), but after this 19 episode run, NBC cancelled the show due to low ratings, and it showed its last episodes as a 1-hour finale, on February 8, 1994. In the finale, Zack and Kelly were preparing to get married. SbtB-tCY was ended abruptly, before Zack and Kelly's marriage could be filmed. So Peter Engel seems to have convinced NBC to let him film a 2 hour TV movie to tie up the loose ends. In the 1994 TV movie, Saved by the Bell: The Wedding, which aired in in primetime on Friday, October 7, 1994 at 8:00 pm EST on NBC, the gang heads off to Las Vegas to witness the marriage of Zack and Kelly. So ended the run of the original Zack Morris based "Saved by the Bell" after 5 years on the air, and more than 100 episodes.
Of course, there was a fourth incarnation of Saved by the Bell: The New Class. But, this was more of a spin-off than a sequel of the original Saved by the Bell.

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