The way I interpret this is #4 is 4 gauge wire which is smaller than #2 or 2 gauge and 4/0 is 4 aught which is huge and bigger than 2/0.
So they go from smallest to largest.
#4
#2
2/0
4/0
I am not 100% sure on this interpretation but someone will correct me if I am wrong.
As far as the small strands vs. the large strands, the small strand #2 will carry more amps and is more flexible than the large strand #2.
I would recommend #2 or 2 gauge.