Nathan,
Both start out in life in similar situations - first papa (bull) gets this glint in his ey...........
Well while that's not entirely wrong, not your question. Both pastrami and corned beef start out the same - cured, pickled beef - usually brisket, but sometimes eye of round or a couple of other cuts. Neither is a description of a cut of meat, but a style of preservation. Where the main difference is that the corned beef will be boiled, sliced and served while the pastrami will be soaked to rid of some of the preserving salt, then encrusted in black pepper and spices and smoked, then sliced and served.
Shakespeare
The Bard of Hot Aire
Pontificator Extraordinaire.