Good question, and you'll probably find the answer very unsatisfying.

They are basically the same thing, with the same responsibilities.

However, "assistant" is usually considered below "associate" in the hierarchy. "Associate" seems to imply that the conductor and associate conductor are colleagues with less social/professional distance between their positions.

Another good question – the music supervisor is the head boss in a music team. The music supervisor is ultimately responsible for all creative decisions, all hiring, all firing – everything. They are above the music director in the hierarchy.

Often the music supervisor on a Broadway show is the person that was the music director or conductor of the show. If the show does very well, and multiple companies (tours, international shows, etc.) are formed, then this person is often promoted to music supervisor and oversees the music for all of the various companies.