Fill-in puzzle
A fill-in puzzle is a crossword grid supplied with the full list of answers instead of clues, so the puzzle is deciding which answer belongs in which slot.
It is the same puzzle as a criss-cross, and which name you meet depends on where the magazine was printed: fill-in is the usual American title, while word fit and kriss kross are more common in Britain. Some publishers reserve fill-in for grids that arrive partly completed, with a word or two already placed to give the solver a foothold.
The method does not change. Sort the answer list by length, look for a length with only one word and one slot, and place it. Every placement fixes crossing letters, and those letters disqualify candidates in the intersecting slots, so the remaining choices collapse quickly once the first few are down. Working in pencil matters more here than in a clued crossword, because a wrong early placement can survive several correct-looking moves before it contradicts itself.
Number fill-ins are the same idea with digit strings instead of words, and they are genuinely language-free.
Criss-Cross Puzzle Maker — the same grid type, built from any word list you give it.