What is the difference in doing push ups in sets compared to all at one time?

Like for example lets say I had a specific number in mind sometimes I like to do sets of 15–20 because usually I can reach it easier.(I take a couple seconds stretch little more, and get some good breaths.)

But if I try to go all out in one burst I tend to not come close at all.I think is it called doing a “burn out”?
Also is it a good for all exercises(push ups,pull ups,etc) to do sets and go all out or always go in sets?
What is better?
Should I do both ways?
And what is the difference in doing them this way or the other?

Thank you.