I guess, to me, the defining characteristic of a "store" is that you can buy things at a store... it just feels awkward to say that a store is just a place that has things and lets you get them on request ;P.
AppTapp Installer was merely a package manager, and they did not implement any store functionality. FWIW, in Cydia's case, I didn't launch "Cydia Store" until about a year after I launched "Cydia Installer".
(AppTapp also wasn't the first package manager for the iPhone, but maybe it was the first one on-device? The one I had used involved USB and some web page I think, but I am forgetting the name.)