I'm pretty sure OCS =/= Leatherneck. OCS is a one or two summer course for MO. Leatherneck is a summer program for Academy types, but is not organized like OCS.
You are correct. Bulldog = Shortened version of OCS for NROTC types. It is run by the OCS Staff. Leatherneck = Shortened version of TBS for Academy types. It is run by USNA Marines, overseen by TBS staff. Some of that staff are handpicked 2ndLt's who have just graduated.
If you want to commission in the Marine Corps, you must do one of them (save for special case exception), depending on your commissioning source. I don't know a whole lot about Bulldog, but for Leatherneck it's an evaluation period and the Marines stationed at USNA assign you a letter grade for your performance during Leatherneck, A-F. If you get lower than a B, you'll be hard pressed to commission in the USMC. Not saying you can't, just that it will be hard. If you get a D or F, forget about it. I got an A. Some of my classmates who were gung-ho, fired up and wanted USMC didn't look too thrilled when they walked out of the office having just found out they got a D. They got motivated about the Navy pretty quick.
As for the handpicked 2ndLt's, they are generally all in the top 10% of the graduating class from TBS. There's also one or two Capt's that are from TBS to oversee the whole thing. I've done it from both sides, as a Midn and as a 2ndLt so I can pretty much answer any questions they may come up about it.
There are exceptions to Leatherneck, but they are far and few between. If you don't want to do it (some sort of once in a lifetime training opportunity presents itself, like an exchange to the Royal Military College, Sandhurst) then the Marine staff at the Naval Academy better know who you are, can recognize you by face and/or name, and you had better get involved with Semper Fi quick.