What is conceivably is so, with some degree of probability; what is possible;
what is not logically inconsistent, but what did not happen in fact; what
may be the case, but is probably not the case.
What might be the case - eventually, perhaps - is in English even
vaguer or more qualified than what may be the case.
There are various logical analyses of "might" and related terms, such as
"may", "could", "would", that are usually rather complicated. Pollock has a
nice set of rules for "might".
It is noteworthy that the word "may" in political, advertisement, legal and
religious discourse is often used to say what may amount to nothing at all, or
mere wind or flatus vocii.