What do you call that carbon copy paper where what you write on the top sheet transfers to the other sheets?

That type of paper is called carbonless copy paper, or non-carbon copy paper, or NCR Paper ( = no carbon required).

You use it when you don't want to copy the same thing twice, or three times, or more, so you just take this paper, with some papers underneath it, and write on the first paper, and everything you write will be transferred onto those papers below it.