It's a children's book, but The Popcorn Book by Tomie de Paola is actually a very comprehensive summary on the history and science of popcorn.
Popcorn pops because the kernels contain small amounts of moisture which, when heated, cook the starches inside the popcorn, causing them to rapidly expand and exploding out the kernel. (This is my basic understanding; I'm sure food scientist will have a more comprehensive explanation).
What this means is that popcorn has to have a few specific features:
- it must have some internal moisture
- it must have a hard outer shell holding in that moisture
- it must not be too moist
I imagine all varieties of "sweet corn", the type used for corn on the cob, would probably not work very well. I don't think it would dry very well, and I think the shell would be weak (a feature when marketing it as something for humans to consume)
Dent corn, the variety used for animal feed, would also probably not work very well. It is a tough kernel and I don't think it would have enough moisture to explode.
I very well could be wrong about this, but I doubt that popping these other types (and I'm sure there are many more) would make for good popcorn.
Interestingly, there are other grains which also pop very well, including sorghum and amaranth.