The needle in a phono cartridge tracks the groove on a vinyl record.
Why does your tone arm need a motor to move it? Is its low friction bearing seized?
I haven't used my Shure cartridge for about 20 years. I think its needle has a weight in the groove of about 2 grams.
Certainly not a stepper (could you imagine a worse choice?), and certainly not a syncronous motor either - it's a simple DC motor feeding a long worm gear, as part of a servo system. The arm has a small amount of horizontal movement, so tracks across the record as normal - at the rear of the arm is a slotted opto-coupler, and as the arm tracks it blocks the slot - this triggers the DC motor which moves the pivot point of the arm to catch back up again. A CD tracks in a very similar way, but with no mechanical contacts or sensors.