4/4 and 2/2 (cut time) are written the same way (four quarter notes or eight eighth notes per measure) but are felt differently. In 4/4 you tap your foot four times per measure (four beats per measure). In "cut time" you tap your foot twice per measure (two beats per measure).
Although they are written out identically, there should be a difference in the way 4/4 and 2/2 (cut time) are played. In 4/4 time, the player should "feel" (accent) each of the beats (1, 2, 3, & 4) in the measure. In 2/2 (cut) time, the player should only "feel" beats 1 & 3.
This being said, almost no banjo player would actually play an up-tempo tune written in 4/4 without "feeling" it as 2/2. Try tapping your foot four times per measure on an up-tempo tune and you'll see what I mean!
Now we'll look at 4/4 and 2/4 time:
From a theory standpoint, there should be little or no difference in sound between 4/4 and 2/4 time, other than tempo, but there is a difference in how they are written.
The reason for using one or the other is a just a notation choice which, hopefully, makes it easier for the player to read (8 sixteenth notes per measure for 2/4 as opposed to 8 eighth notes for 4/4). Most players find it easier to read a measure made up of quarter and eighth notes (4/4 or 2/2 time) as opposed to eighth and sixteenth notes (2/4 time).
Hope this isn't too confusing...
Most tabs are written out to be played in "cut" time (2/2). It's read the same as 4/4 but with only two foot taps per measure!
Thanks... Mike