What are the differences between the book and TV Series for Drummer's Storyline?

Your memory of Drummer's character from the books is correct. In the TV show, Drummer's story is a collection of elements of the storylines of multiple characters from the books:

• Michio Pa: executive officer of the Behemoth (under Klaes Ashford) in the book Abbadon's Gate, whereas in the show Drummer is the captain and Ashford is second in command.
• Carlos "Bull" c de Baca: chief security officer and third in command of the Behemoth in Abbadon's Gate who sustains a spinal injury due to the sudden introduction of the slow zone, whereas Drummer sustains a similar injury in the show. Bull appears to have Drummer's role as security officer of Tycho Station in the fifth season of the show.
• Sam Rosenberg: in the books she is an engineer who worked to repair the Rocinante and became Naomi's close friend in the process, but in the show her story is largely taken over by Drummer.

The show probably modified Drummer's story in order to avoid introducing (and casting) so many relatively minor characters, but that's just a guess.