Five Canadarm robotic arms were built. Five space shuttle orbiters were flown to space.
Did each orbiter have its own dedicated Canadarm? Or were they rather moved around from orbiter to orbiter, based on whatever equipment was ready at the moment?
No, they were not dedicated (except for 302 to Challenger, but that was a fluke, it was not the original arm on that Orbiter).
They swapped 'em around but not at random - if it made sense to leave them on an orbiter, they did.
I won't go through the whole history, but look at some early flights:
Orbiter scheduling was complicated and they wouldn't leave an arm sitting in Palmdale while the Orbiter was down for extensive maintenance. Some of the complications of scheduling are discussed in the answer to this question: Why was Space Shuttle Atlantis selected for Mir docking so frequently? (You can see RMS annotations in the charts in that answer as well - in the second chart you can see Discovery fly with 301, 201, 201, 303, 301 - excerpt below, purple arrows).