Yes, there is. I think it might be a bit difficult to hear at first, but I think you should go on www.dictionary.com, find both of those words and listen to them! They have that option on there. Maybe that would help.

Yes, there is a difference. For the word "man", we pronounce it with a sound between "e" and "a", we pronounce "e" with the mouth open as if you want to pronounce "a".

There may be some dialects that pronounce it the same, but where I live (Ohio in the U.S.) there is a difference. My lips spread out farther to the sides to produce the vowel in "men" than the vowel in "man."