in the uk we tend to use 28gr (1oz) 7.5 shot for clay shooting. soe loads are also available in 21 and 24 gramms (3/4 and 7/8).In general, hunting loads have more powder and more shot than the usual skeet or trap loads.
Waterfowl hunting, nowadays, mandates non-lead shot by law. A very few places have that restriction on upland birds. Skeet and trap don't. Most dove and quail areas allow lead shot.
And then there's the somewhat specialized stuff. For instance, in hunting blue quail here in the desert, shots are commonly around 40 to 50 yards. They run before they fly, so it's a case of shoot through grass, quite often. Shots at birds in flight are common at 50 yards.
So, my usual load is the Winchester hi-brass. 7-1/2 shot. 3-3/4 dram equivalent powder, 1-3/4 oz. of shot. FWIW, from my full-choke Model 12, it accounted for a one-shot, DRT kill on a bobcat at 25 yards.