It seems that although these terms are academically respectable within the study of linguistics, some people consider them insulting.

From this site.

Pidgin and Creole Languages
Originally thought of as incomplete, broken, corrupt, not worthy of serious attention. Pidgins still are marginal: in origin (makeshift, reduced in structure), in attitudes toward them (low prestige); in our knowledge of them.

Some quick definitions:

Pidgin language (origin in Engl. word `business'?) is nobody's native language; may arise when two speakers of different languages with no common language try to have a makeshift conversation. Lexicon usually comes from one language, structure often from the other. Because of colonialism, slavery etc. the prestige of Pidgin languages is very low. Many pidgins are `contact vernaculars', may only exist for one speech event. Creole (orig. person of European descent born and raised in a tropical colony) is a language that was originally a pidgin but has become nativized, i.e. a community of speakers claims it as their first language. Next used to designate the language(s) of people of Caribbean and African descent in colonial and ex-colonial countries (Jamaica, Haiti, Mauritius,Réunion, Hawaii, Pitcairn, etc.)

Relexification The process of substituting new vocabulary for old. Pidgins may get relexified with new English vocabulary to replace the previous Portuguese vocabulary, etc.

Some mainstream languages may have arisen by this process. For example, French may be considered the result of contact between popular non-literary Latin, as spoken by Roman soldiers, and the Celtic speaking native peoples. Later an addition of Germanic languages from the Frankish invaders were added. The whole process took place in the spoken language, while written language, where it existed, continued to be Latin. English itself is the result of contact between the Anglo-Saxon peoples, the native Britons and the French speaking invaders. Some pidgins evolve into more or less standard new languages, others become influenced heavily by an established standard language. Some studies show Jamaican varieties becoming closer to mainstream English.

The variety spoken in the coastal districts of West Africa (Nigeria, Ghana, Sierra Leone, Liberia) may be establishing itself as a new language. It already has some literary expression. The variety spoken in Papua New Guinea has achieved literary expression (Tokpisin)

Are any of these languages likely to become standard languages in the manner of French and English? Who can foresee the future? Some of them, under the influence of modern electronic media, may be evolving towards one of the existing standard languages.