I don't think that (a) has the distinction of "making it just in time" because it says "The movie had started when I got to the theater" (indicating a state that began before the speaker entered the premise). For such a meaning, simply saying "The movie started when I got to the theater" would indicate that you made it just in time.
That being said, I think that (b) does have the same meaning as (a), but in some cases (depending on the context) you could use (b) to indicate a sense of remorse/frustration/surprise as it relates to the speaker directly.
e.g., "My friends and I decided to arrive a few minutes early to get good seats, but the movie had already started when we got there."