It does matter because the sheath of the wire is what dictates its current carrying capacity. Different materials have different ratings in voltage and heat. You size your wire for your load. Now given the information you provided, I have no idea if it will impact your setup or if it actually will matter in your given case. It probably doesnt but I cant say I would want my system setup with under rated cable. I would probably just buy whatever rating was on the factory wire or better.
Its not totally relevant but take a look at table 310.15 from the NEC.
This shows how a wires ampacity needs to be derated based on its jacket rating and ambient temps.
but wait theres more
This shows how the same gauge wire has different amp ratings based on jacket type.
Really you need to figure out what your realistic load is, then figure out what youre ok with amperage wise. NEC says size your stuff for 1.25x your load…but take that with a grain because the NEC is written for the kind of wiring in your house. It does serve to show that ratings do indeed serve a purpose.