What Is Shareware?
In 1982, a couple of programmers, Andrew Fluegelman, a California programmer, wrote a well-known MS-DOS communications program called PC-TALK III. After failing to find interest from traditional distributors, he decided to give the software away and ask for a donation from anyone who liked the software. He called it "freeware" and even trademarked the name. This stopped others from using the term for marketing without his permission. He did not continue developing the software and was not very successful. The trademark wasn't enforced after his mysterious disappearance and presumed death in 1984 (src:The Jargon File).

Around the same time, Jim Knopf (also known as Jim Button), a programmer in Washington state, wrote a program that was initially a mailing label program, EASY-FILE and marketed as "user supported software". He also decided to give the software away and ask for a donation. Button renamed the program to PC-FILE. He did very well with the product mainly because he continued to add features.

In 1983, Bob Wallace, came out with a word-processing program, PC-Write that he sold as "shareware".

Other smaller programs appeared and they were distributed as either "freeware" or "user supported software." Unfortunately, they could not legally use the term freeware since that was a trademarked term. The term user-supported software was too cumbersome. A magazine contest to name the marketing method selected shareware as the favored name. Bob Wallace, the first nown user of the term, said it was okay for anyone to use the name.

There is controversy over who originated the shareware concept, Fluegelman or Button. For this reason, they are listed as co-creators.

Definition of Shareware
Software that you are allowed to use for a limited period of time while you evaluate it. If you decide to continue using it, you are obliged to adhere to the license agreement.

Different variants of the way shareware authors collect their registration fees, also added additional names that shareware is known by. The incomplete list.

Adware

A relatively new form of freeware that appears to be free. Advertisers pay to have advertising banners show up while the user is using the product. The ad software periodically checks on the Internet for new advertisements. Many adware software is also spyware.

Careware

Shareware that requires that some or all of the registration fee goes to charity. This is also refered to as charityware.

Crippleware

Shareware that allows full usage of some features but requires registration to enable other functions, crippling the program. Some crippleware may restrict necessary functions like save or print. Other software is still extremely useful even without the registration, only advanced features are crippled.

Freeware

Free shareware that, the author does not require the user to pay any fee. Often the free version has restrictions like only being free for personal use, commercial use requires a registration fee.
Initially (and probably legally), this was a trademarked term synonymous with (and requiring a fee).
Note that this is not necessarily public domain software, the author still owns the rights. The author has just given permission for free use.

Guiltware

A piece of shareware that complains that the author is suffering because you have not registered after the trial period ended.

Nagware

Shareware that pops up reminder screens when the program is started or ended. It normally requires the user to click a button or certain keystroke before continuing.

Payware

The shareware industry wanted to give another name for the traditional commercial software. They came up with the term payware.

Postcardware

Shareware that borders on freeware, in that the author requests only that satisfied users send a postcard of their home town or something. (This practice, silly as it might seem, serves to remind users that they are otherwise getting something for nothing, and may also be psychologically related to real estate "sales" in which $1 changes hands just to keep the transaction from being a gift.)

Spyware

This freeware tracks your activity and reports back via the Internet so that you can be targeted for specific e-mail advertising. The biggest objection to this is that users are not told that the spying is taking place.

Trialware

Shareware that works perfectly and completely during an evaluation period (either a number of days or a number of uses) and then stops working until a keycode is entered. This keycode is obtained when the product is registered (and a fee paid).