IDC - Insulation Displacement Connector - means that when you jam the wire in, it forces the tabs to cut the insulation and make contact with the wire.
Crimp and stuff (Molex) - means you crimp a terminal onto the end of the wire and then stuff it into the housing
They do the same thing slightly different ways. Both will fit onto the same headers.
You are right that you need to match the size though.
You might need this one, if you damaged the tabs on yours. https://www.pinballlife.com/index.php?p=product&id=4152