Pretty much, except for magazines obviously for the 9mm, and if you want full capacity 7.62x39 then specific magazines for them as well... (I think the 7.62x39 pistol mags fit 12-ish rounds of .223 though)
The only difference is that you MAY need a heavier buffer for the 9mm, however they change out easily as well.
Other than those, you're pretty much spot on though, 1 registered firearm component (The lower) and a bunch of different uppers you can swap out at will! One of the strong points of the AR platform, is the upper/caliber interchangability.