The motors on the feed and takeup reels are constant torque. For compliance there is a tape tension swing arm between each reel and the capstan that drives the tape. The capstan has a massive flywheel attached to lower the Flutter and Wow.
The free standing tape recorders used with computers are optimized for the highest possible speed of access. They can not afford the mass of the tape tension swing arms and have replaced both of them with a small elevator shaft like compartment where the tape hangs. There's a control system that drives the reels to maintain the loop in the elevator compartments.
Telephone \ Poulsen Telegraphone