OK let's set the record straight. "Corning" beef is a curing process for really any type of meat, but most folks seem to like brisket the best. It involves adding the meat to a salt solution. We also add pink curing salt which does two things, it fights the bot bug and turns the meat that delightful pink color. Other than that most folks add sugar and some sort of pickling spices, but that's a personal preference.
Now there are two things you can do to corned beef, you can boil it or steam it and eat it as is. Or you can smoke it and/or steam it and it becomes known as pastrami. The smoking can be like conventional brisket smoking or it can be done in the sous vide process as I posted earlier this week.
Either way, corned beef and pastrami are essentially the same thing, just cooked differently and thus acquire different names.