What do you call a rotary switch that does not have a max turn degree?
You call that rotary encoder.

A rotary encoder basically transforms (encodes) angular position or speed into an electronic signal.

There are tons of types of encoders, you can divide them in absolute and relative, or incremental.

An absolute encoder will give you the position of the shaft relative to an absolute reference. Since these encoders must implement some sort of memory, to keep track of the distance from the reference, they are usually limited if not physically at least logically.

An incremental encoder is useful just for difference between positions, it can't tell you the distance from a fixed reference. The prince of all the incremental encoders could be find in old mouses, the ones with the small, heavy ball that you should always clean. It consists of a disc with several fissures, an LED and a light detector. When the disc rotates it shuts covers and uncovers the LED producing a signal that can be measured from the light detector to compute the shaft speed. The direction of the rotation can be calculated thanks to a second detector, slightly off phase. The two signals together allow to calculate both speed and direction.

The encoder you are referring to is probably a digital mechanical encoder: the shaft is fixed to a disc made of an insulating material, on said disk there is a unique pattern of contacts made of some kind of conducting materials. Fixed with the casing there is a sort of "contacts comb" that can sense the metallic pattern and tell where the shaft is positioned.