Actually, these terms are set by law.
If you remove the top sell from a crab and clean out the entrails and stuff and then cut in in half so you can view a cross-section, what you'll see are a series of tubular compartpents containing the flesh.
Those towards the back, near the swim fins, are small, and the meat is kind of broken up looking before you even remove it. That's the backfin meat. No matter how small a pick you use, it's almost impossible to recover that meat in one piece.
As you move forward, the compartments get larger and the meat more cohesive. That's the lump. Extra large lump comes only from the very frontmost compartments, and the size of the piece determines if you can use that classification. Extra large lump is actually more prevelant now than it used to be because there's a minimum size on crabs, and, overall, larger ones are being harvested.
Claw meat, obviously, comes from the claws, and is considered by most crab fanciers to be more grainy. As Blue Zebra notes, it's usually used only in cooked dishes. But not always. Some folks think a bowl of melted butter and a bowl full of crab claws is the cat's meow. And the claw meat makes a nice accent piece in soups and chowders.
I think the objection to pastueurized crab is more theoretical than real. All crab you buy---whether "fresh" "pasteurized" or in cans or pouches already is cooked. Pasteurization just gives it a longer shelf life. And, for anyone who lives inland, that's pretty much the only way it's available.
They have taken the oath of the brother in blood, in leavened bread and salt. Rudyard Kipling