There are hand and air hammer chisels – and rarely should the two meet. That is an air hammer chisel should never be struck by a hand-held hammer. That distorts the shank of the chisel which, in turn, distorts the piston of the air hammer (very serious). There is a striking cap that can be placed over the air hammer chisel to protect it, though.
Stone carving chisels can have steel or carbide tips. Steel ones are sharper but need to be sharpened more often. The carbide ones are much stronger but because of the carbide insert they are “fatter.” On softer stones, the steel chisels produce cleaner lines. On harder stones, the carbide ones make more chips. Note that carbide is a brittle metal so protect these valuable tools from dropping on concrete or smacking against each other.
When using chisels stone must be coming off. If the chisel is held too steeply into the stone (like 90° )the chisel may break. If the chisel is held too acutely (like 15° ) it will just glide over the stone. Experiment with angles until you are actually carving. Never, ever use a chisel as a pry bar or try to knock off too big a chunk.