I am confused whether a lead screw and a worm screw are the same exact thing. In my engineering workshop lab, they come up as separate things. For example, a worm screw is there in the indexing head of the milling machine (as part of the worm drive), while the lead screw is part of the feed mechanism in the milling machine and the lathe machine. They both look like the exact same thing. Can someone tell me what's the difference? https://en.wikipedia.org/wiki/Leadscrew https://en.wikipedia.org/wiki/Worm_drive
One way to think of it is this:
A Worm, it's a short "threaded cylinder" with relatively few teeth. This rotates and in doing so, moves a worm wheel with much more teeth than it. Typically this results in a rotating motion as @Eirc Shain suggested, but it could also be used to drive a long Rack (see 'Rack and Pinion') in a linear way. If the rack has more teeth, and it's engaged "from the side" and not wrapped around the threaded cylinder, then that cylinder is a worm. While it may look like a thread form, it's actually more correct to think of them as elongated teeth, with the number of thread starts being effectively the number of teeth.
On the other hand, a lead screw is much longer and with more thread turns than the item that engages with it (usually a nut or a half nut), and that engagement wraps around the cylinder. This always outputs a linear motion.
Does this make things any clearer?