Yes, Wales is generally divided into North, Mid and South (and Corner, as in Cornwall).

South Wales generally corresponds with the former Kingdom of Deheubarth. https://en.wikipedia.org/wiki/Deheubarth?wprov=sfla1

Deheubarth was punished for rebelling against Engkand in 1282 by being divided into the three counties of South Wales. Referring to it as South Wales rather than south Wales is a miniature act of rebellion in itself; the Welsh government styles it capitalised to emphasise that historical distinction; the Britsh government uses lower case to erase the distinction.