Patois, Patwa, Patwah, Jamaican Creole, Jamaican. People use all of them and argue about which is correct. Short answer: they are the same language, and which word you reach for says more about the setting than the speech.
The commonest spelling in English, borrowed from French, where it means a regional dialect. It is what most Jamaicans write when writing in English, and it is what you will meet in newspapers and on the packaging of things. Pronounced “pat-wah”, which is why the next spelling exists.
The same word spelled the way it sounds, under the Cassidy-JLU system, where one letter carries one sound. Nothing about it is informal. It is the spelling you use when you are writing the language rather than writing about it in English. Patwah is the same instinct with an English habit left on the end.
The term in linguistics. A creole is a language that grew out of contact between others and then acquired native speakers — people who grow up with it as a first language. Jamaican Creole has millions of them.
No, and the difference is not a matter of respect. A pidgin is a contact language nobody speaks natively — a working arrangement between groups with no shared tongue. When children grow up speaking it as a first language, it stops being a pidgin. Jamaican passed that point generations ago.
It shares most of its vocabulary with English, which is what makes people assume so. The grammar is where the assumption breaks. Tense and aspect are marked by particles in front of the verb rather than by endings on it. Pronouns do not change for case. There is no verb “to be”; there are three different constructions doing that work. A dialect of English does not restructure the verb phrase.
The Jamaican Language Unit at the University of the West Indies at Mona publishes a standard orthography for it, and the New Testament has been translated into it in full. Those are not things that happen to accents.
Patois in English prose, because that is what people search for and say. The popular spelling in the lessons, because that is what you will meet in messages and music. Cassidy-JLU shown beside it, because it is the one that teaches you the sound.