I used to believe the answer to this question was "No", that corned beef and pastrami were always cured differently and were distinctly different products. However, in speaking with experts, I've learned that often times corned beef and pastrami both start out the same way—cured using the same liquid injection or the same dry curing process. It is only after the curing process that corned beef and pastrami diverge in terms of their seasoning and cooking method.
Corned beef—usually a whole brisket, brisket flat, brisket point, or bottom round—is seasoned with pickling spices that may include any or all of the following: cinnamon, allspice, mustard seed, coriander, bay leaves, ginger, chilies, cloves, black pepper, mace, cardamom. Traditional corned beef is then boiled slowly for several hours over medium heat.
Pastrami—usually a whole brisket, brisket flat, or bottom round—is seasoned with ground black pepper and ground coriander. At some of the famous New York City delicatessens, pastrami is made using beef navel (a cut located on the underside of the cow, starting where the brisket ends) that is smoked at low temperature for a few hours, then steamed to complete the cooking process. On the WSM, we smoke pastrami at 250-275°F to an internal temperature of 195°F then let it rest for two hours, at which point it is fully cooked and ready to eat.
Most corned beef and pastrami is injected with a liquid cure—it's fast and can be automated by machine. Some pastrami is dry-cured, as in the Pastrami article. In my opinion, this results in pastrami that tastes more intense and less like corned beef.
Around St. Patrick's Day, some WSM owners like to make quick pastrami using the corned beef briskets that are so abundant in supermarkets at that time. You can read about this in the Quick Pastrami - Smoked Corned Beef article.