You might want to study for the exam.
We may have dinner at 7 PM.
I might can help you.
✅ CorrectI might help you.
She may can join us.
✅ CorrectShe may join us.
I may to go.
✅ CorrectI may go.
While they are similar, "may" is often used for more certain possibilities, while "might" suggests less certainty.
Yes, "may" is considered more formal than "might."