This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
We don't really refer to anything as "being locked." Rather, we say that we obtain a lock. But if by "locking X" you mean "obtaining X's lock", then, yes, you're correct. The object whose lock we obtain is the one whose synchronized method we are executing.
The above methods are equivalent. Both obtain the lock for the "this" object and hold it for the entire body of the method.