Finitism is a derived term of ultrafinitism.

In mathematics terms the difference between ultrafinitism and finitism

is that ultrafinitism is a form of finitism that is even more extreme in that it denies those constructs whose construction cannot be physically performed (such as a number that no human could have time to calculate) while finitism is an extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps.