All the T.T. I worked on they were synchronous motors, for US/UK use a drive pulley could be obtained to change the rpm.
Later turntables tended to use small DC motors, or BLDC ones (probably one of the earliest domestic uses of BLDC - along with tape recorders).
Many of the small DC motors had the speed control electronics inside, with two presets (for 33/45) accessed via small holes in the casing.