Triple 7 or pyrodex are just a brand name pellet style powder. Most hunter use 2 50 gr pellets. You can also use loose powder if you want. I use pellets just because of how easy to use they are. No measuring needed.
T/C shockwave, Hornady and Powerbelts are different brand names of bullets. Hunters use a different weight bullet for whatever their desires are and for what shoots more accurately out of their gun.