***not a teacher***
Context, in linguistic terms, refers to the words or phrases next or close to a piece of utterance you're focusing on. The context can help us get the real meaning of that utterance in the situation it is used, which in turn helps avoid ambiguity. (For example, if you want to teach/learn a new word, you'd better, it's said, contextualise it; that is, you'd better put it in a meaningful context.
I suppose co-text means the same except that it may also be used to refer to the discourse you've extracted that utterance from (and not necessarily the immediate or surrounding words).
Let's be hopeful for complete answers.
Interested in Language