Southpaw/Orthodox refers to which hand your leading with.
Positioning yourself so that your right is your jab = southpaw
Positioning yourself so that your left is your jab = orthodox.
I like orthodox because I always thought my left hook was my best punch. For a 3 punch combo I could end with my hardest shot (left hook) jab, right cross, left hook.
But, being a southpaw in a sport with more orthodoxes has it's benefits.
Casamayor's a southpaw and when he fought orthodox boxer Michael Katsidis he exploited an opening that can present itself to a southpaw fighting an orthodox.... straight lefts right down the middle.