May and might have the same meaning when used as a modal (or helping verb.) Examples: She may go shopping. She might go shopping. The only difference is may is slightly more formal to some people. Many people use might more often in speaking and may more often in writing. But they can change depending on the person and their mood.
Remember, though, may is also used to asked for permission. Example: May I use the telephone? It is very rare to use might to ask for permission.