Yup. For all reel-to-reel tape decks, the main speed control keeps the capstan at a constant RPM, such that the tangental velocity of the side of the capstan is constant. I recall working on some big Studer-Revox decks that had a detailed procedure for adjusting the motors that turn the hubs for both the take-up and supply reel, maintaining a small but constant tension. The take-up reel would exert more tension than the supply reel, but not so much that it caused the tape to slip through the capstan and pinch roller. The capstan actually served to turn the rubber pinch roller, which it contacted above and below the tape itself. The rubber pinch roller in turn pulled the tape through, so it was important that the rubber did not become dirty or "glazed". Motors that drove the reels also required separate tension adjustments for fast-forward, re-wind, braking, or "scrub" functions during which the pinch roller was not engaged.
Cassette decks are more likely to have pullies to turn the take-up spindle, while the supply spindle would merely depend on friction to keep tension.
Vinyl turntables typically either had a direct-drive central axle that was controlled for constant RPM, or else some drive-wheel that pushed the inner surface of the edge of the platter through an intermediate rubber wheel, or a belt-drive to a pulley on the centre axle. Some speed control schemes involved a pattern of stripes on the inside of the rim and a light bounced off them onto a sensor which would tell the control circuit what the tangential velocity was. Since the sensor does not travel inward with the tonearm, it's still aimed at keeping a constant RPM.
VHS (Vertical Helical Scan) video tape drives also use a capstan and rubber pinch rollers to transport the tape slowly from one side toi the other, but the record/playback head is more exotic (than for audio tape), being on a spinning drum that is slightly tilted so that the head makes multiple diagonal passes across the tape. It has its own speed control circuits. It gives the same effect as running a reel-to-reel at much faster speeds without having to make a huge-diameter reel for the tape.