i understand that 2/2 or cut time has 2 beats as opposed to 4/4 or common time, but how does this actually sound different? if you took a piece and played if it was notated as being 4/4 and then played it again where it was notated as being in 2/2 but played it at the same speed etc what would be the difference?

and is it possible to hear a piece and be able to tell whether its 2/2 or 4/4? how can you hear the difference?