Agree with Leslie. Add: I may go to the store OR I might go to the store. means: I probably/possibly do sth, not sure You may go to the bathroom. means: you could/can do sth, you are allowed to do sth

Well. They both can mean the same thing like: I may go to the store OR I might go to the store. But may can be used in other ways like: May I have a pencil OR You may go to the bathroom. But might cannot be used like that.

as has been said and more over the word might sometimes is used in the past tense