You can search in parallel, but a depth N search can only become a depth N+1 search after the depth N is done (i.e. sequentially).

In any case the name RSI has stuck - the idea doesn't change or make any more sense by giving it a different name.

Because "depth" is recursive.

You can search twice without waiting for the results of your first search: iteration.

You can't if the thing you need to search for is the results of your first search: recursion.