For me, could suggests some idea of circumstances permitting a possibility, might simply suggests the possibility:
Bill (Looking at a slightly fuzzy photograph of a group of people): Who's that person standing next to Mr Jones?
Ben: It could be my sister. (Ben knows that his sister was in the area at the time, and the person standing next to Mr Jones has long blonde hair, as does his sister.
For the record, and for the sake of understanding what each of us means, I want to point out that this is the difference that I refer to as
theoretical versus
real possibility. Your 'circumstances that permit the possibility' is what I understand as the 'theoretical framework' with which we construct hypotheses, whether that's through empirical evidence or through purely rational deduction. In other words,
It could be my sister is another way to say 'It is theoretically possible that it is my sister, given the evidence at hand'.
Contrastingly, where you say '
might simply suggests the possibility', I'd say
might expresses a 'real' possibility (as opposed to hypothetical one).
Bill: (Looking at a slightly fuzzy photograph of a group of people): Who's that person standing next to Mr Jones?
Ben: It might be my sister. (Ben is saying that it is possible that it is his sister. It is also possible that it is not.)
In my terms, the use of
might shows that the speaker is focused on the reality of the matter. Ben's talking here about what
is true rather than what
could be true. In other words, this utterance is not a statement of theory but a statement of reality (or uncertainty about reality). This is all quite hard to explain, but I hope I've made it clear, or clear
er, what I mean when I use the term 'real' possibility in past and future posts.
So to echo what we all seem to agree on:
modal verbs do not express in themselves degree of possibility. Degree comes from other words and phrases (typically adverbs and adverbial phrases). However, in my understanding, modal verbs can express a difference in
kind of possibility.