To start with, what is thrust? The answer is "the reaction force generated when force is applied in a certain direction".
For example, the jet engines of a large airplane generate jet in the backward direction to push the airplane forward using thrust.

A ball screw is a mechanical element that converts rotational motion into linear motion; so, when the screw shaft is rotated, the nut is pushed forward (or backward). As a result, thrust generated in the nut works by pushing the table (load table) attached to the nut housing.
Thrust can be generated by many other mechanical elements as well, such as slide screws and air cylinders used in compact jacks for cars.

Then, why aren't ball screws used in compact jacks?

Hint: Because the "ball screw has excellent mechanical efficiency" and "allows for accurate control".
If a ball screw were used in a compact jack, the jack would go down swiftly as soon as you take your hand off the jack handle because its mechanical efficiency is high. However, a jack using slide screw will not go down naturally even if you take your hand off the jack handle because the jack is made by taking advantage of the low mechanical efficiency of the slide screw.

In the case of an air cylinder, its shape is similar to that of a syringe, and generates thrust by compressing a fluid such as air in the cylinder to push the piston. Its advantage is that it is cheaper, and the study of its specifications easier when compared with that of a ball screw. However, since complex conveyance and positioning are difficult with air cylinders, they are mostly used in simple applications involving fixed-stroke, reciprocating motion. Ball screw "thrust" is suited to applications where you want "to move more smoothly with the same force" & "to position accurately and use various strokes". For these reasons, they are used in semiconductor manufacturing equipment, industrial robots, and conveyance and positioning of machine tools,

As seen in these examples, there are different mechanical elements that "generate thrust". Since the one to use is chosen depending on the required functions, cost, and features, it may be interesting to look inside various machines and equipment.