Linear Electric Motor

[TimFox]

I agree that a "motor" produces motion.
There are specific types and applications of motors that have specific names, such as "actuators" for motors that operate between two positions.

[CaptDon]

Another really cool 'motor' I have seen was used to make the flippers move on one particular type of pinball machine, sadly I forgot which one although from around the late 70's. It was an electromagnet about 1.5" in diameter with a shaft going through it. The shaft has a spiral groove which caused the shaft to have a rotary motion against a fixed pin protruding into the groove. The end of the shaft above the playfield had the flipper on it and the end of the shaft sticking below the 'motor' had a somewhat thick round disk on it that would be attracted to the electromagnet causing the flipper to move. In the schematic the device was actually called out as a flipper motor. At the end of the day, they really didn't work very well and didn't have a lot of power. A conventional solenoid flipper retrofit kit was soon released and those whacko rotary solenoid flipper motors went directly to the trash bin. I suppose an unmodified pinball machine would actually be a rare collectable these days??

[TimFox]

In commercially-available solenoid activators, there are both linear and rotary types for different applications.
A useful general description of solenoids:  https://www.kendrion.com/fileadmin/user_upload/Downloads/Datasheets_Operating_instructions/Electromagnets_Actuators/Electromagnets-Actuators-Technical-explanations-EN.pdf