What is the difference between cut-time and 2/4?

Answer 1

There is definitely a difference between cut time and 2/4. 2/4 is 2 quarter notes to the bar.
Cut time is essentially a 2/2 signature. There are still 4 quarter notes to the bar but it's played double time of 4/4, so quarter notes are played as eighths, half notes are played as quarters and so forth.
When you're counting 2/4 you just count 1,2 1,2. But it should still have the feel of playing in 4. Cut time is still counted in 4 (a very fast 4, admittedly), and it generally has the feeling of playing in 2, just because it's double time. Does that make any sense?

Answer 2

nothing technically just the way that you think about it