I have a question about squad swarm that came up in a skirmish recently.

Do the two groups have to be named exactly the same (but allowing for regular and elites), or can they both be, say, troopers? For example -- heavies and snow? We played it according to the former. Was that correct?

Former, names have to be exactly the same

Trooper is a trait , not a deployment card / group name. (See Elite Figure from RRG, there's something in unique allies also, I think.)