My mother tells the story of when she first married and wanted to cook something special for my father. She went to the butcher and asked for a "beef chop" and was taken aside and given a lesson in the various cuts of meat. At least in the UK, "beef chops" do not exist. The same cut is called a "rib of beef". As far as I can judge, however, the "rib" only refers to the first few neck-end ribs. The rest are the various sirloin cuts.
Steaks on the other hand can be rump, fillet, chateaubriand, sirloin (minute and porterhouse) or entrecote. Porterhouse steak cooked on the bone is known as a T-bone in the States. Some correspond (roughly) to "chops" without the bone and some do not.
for the various cuts of beef.
Chops, as Ken has already indicated, always refer to cuts served on the bone, and generally nowadays from the ribs, of pork and lamb in particular, but also veal. In the UK at least, chops and cutlets are different cuts. Chops are from the loin and cutlets from the neck end.
Cuts of pork are shown here
Cuts of lamb here
Purely as a guess, I would assume that "chop" derives from the method of cutting the meat, or more to the point, the bone, namely with a chopper. In that event, it would ultimately derive from Old French coper
(modern French couper
). Perhaps that association has been lost with beef, as the cuts are less frequently served on the bone.
Steak is indeed probably from Old Norse, and unless I'm mistaken cognate with the word "stake", both going back to the idea of a pointed stick (in our case, the "spit" used to roast the meat).