The big issue with corn is the germ, which is relatively high in fat (at least compared to other brewing grains).
Flaked maize - this will always have the germ and the husk, removed. It is basically pure corn endosperm, which is mostly starch and a small amount of protein. It contains very little fat.
Corn meal - this may or may not have the germ, the husk, or both, removed before being ground. If you find cornmeal that is ground from de-husked and de-germed corn, it should behave much like flaked maze after a cereal mash (as you rightly predict). If you happen to use whole cornmeal (which includes the germ and husk) it will not give the same result as flaked maize. The corn flavor will be different, probably more pronounced, though maybe not hugely. With whole cornmeal, the fat from the germ may tend to go rancid, so make sure it is fresh. It may also have a negative effect on the foam quality of the resulting beer, though as long as you don't run off very aggressively this impact may not be too bad. It's going to depend on how much you use and how you treat it, though. Certain lipids, when oxidized during mashing, also lead to cardboard-y, stale flavors in finished beer, detectable at one part in ten billion, so even minute increases in lipids can dramatically effect the flavor stability of your finished beer. The fine grinding of the germ, if present, will do nothing to help this situation. I'd expect a beer made with whole cornmeal to lose its freshness pretty fast, depending on the proportion of corn used.
Popcorn - Same as whole cornmeal, this will contain the germ and the husk, and as such will probably give you a more 'robust' corn flavor. See this related question for some first-hand experiences. I imagine that, since the germ tends to remain largely within the husk in popped corn, and neither will be ground, it shouldn't give you too much trouble in terms of head retention or off-flavors (see above, re: whole cornmeal).
That being said, I don't see any real reason not to experiment with any of these, just be aware of the potential issues when using whole cornmeal.