This is a source of confusion but it shouldn’t be, because the difference is clear-cut!

As usual, I am not going to provide a grammatical analysis. Instead, we’re just going to look at some typical sentences together.

Read the sentences carefully and make sure you understand them, then repeat them aloud a couple of times, play with them and try to make similar sentences (you can do this in the comments), and finally tuck them somewhere safe in your brain for future use. 🙂

It will rain tomorrow.
It will probably rain tomorrow.
It may rain tomorrow.
Maybe it will tomorrow.

There is a chance that I will be late for tomorrow’s meeting.
Maybe I will be late.
I may be late.

Hopefully things will get better.
Things may get better.
Maybe things will get better, maybe not.

There were maybe twenty people at Jane’s party. I’m not sure really. There may have been more.

Will you marry me?
Maybe… I don’t know.
Please! You know how much I love you. I’ll do anything to make you happy.
I don’t know. I may accept to marry you, or I may not. I need time to think more about it.

Can this be repaired?
Maybe. I’ll see what I can do.

Are you still having pain? Maybe we should call a doctor?
No, it is not necessary. It’s nothing serious. It’ll go away.

It will rain tomorrow.
It may rain tomorrow.
Maybe it will rain tomorrow.

It will be cold.
It may be cold.
Maybe it will be cold.

Maybe you should now repeat the above sentences a few times? It may also be a good idea to try and make some similar and realistic sentences…