A 35 mm movie frame is the same dimension as half-frame still images; the simplest way to get a still from that is to put it in an enlarger. For smaller sizes, you can still enlarge (I routinely enlarge 16 mm film, with a frame size not much different from modern Super 16), though 8 mm film is rather tricky to handle. Since most movie film available to the public is positive print stock, you'd need something like Ilfochrome to get a positive print, or else you'd need to make an internegative and print from that to produce a B&W print.
Another simple way to pull a still from cine film is to project the film using a projector with freeze frame (this, among other things, may dim the projection light to prevent heat damage to the film frame in the gate) and simply photograph the projection screen from a vantage as close as practical to the projector lens (to minimize geometric distortion such as keystoning).
The movie publicity stills you usually see, however, are originally photographed as still frames, using a still camera (used to be a Speed Graphic was used a lot for this, but these days they're probably mostly digital). They're posed, static scenes, for the most part, though it's not unheard of for a production's still photographer to shoot on the set during run-throughs or even actual takes (the latter tends to get him in trouble with the sound people, however, especially if he uses an SLR with the noisy mirror slap).
However -- the device you describe sounds more like a slide duplicator, and such a device would work fine for making printable negatives from cine film frames. No need to reinvent it; you can get these on eBay every day for either M42 or K mount.