Welcome to DC.
Historical distinctions aside, corned beef and pastrami are very similar. Corned beef starts out as brisket (usually) that is soaked in a brine to cure it. Then it is cooked and eaten. If you take a corned beef before cooking, coat it with a certain blend of spices and smoke it, you have pastrami. So, in short-hand, pastrami is seasoned, smoked corned beef.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan