Is slow motion dictated by shutter speed?

Ah. First off, thank you for the well-explained, informative replies. That was my intuition, but I didn't even know that one could record at higher than 30 or 60 (and maybe you can't on a standard DSLR, can you?). That makes sense; I thought it was done in post, but now that I think about it - it would be impossible. 30 frames in a second is 30 frames in a second. If you slowed down 30fps 10x, you'd just be showing each frame for 1/3rd of a second which would look more like a slideshow - not slow-motion.