You are right, and I'm sorry to have been somewhat opaque in my presentation. Optically, the aperture size (from which F-stops are calculated) is the size of the light-gathering element. Meanwhile we simultaneously have a mechanical aperture that controls the amount of light entering the lens that is transmitted to the film plane. As photographers, we tend to think of the mechanical device as 'the' aperture, since that's where the aperture-based exposure control happens.
I've probably made this even more confusing...short version...Helen is right.
And now to wander way off topic, I've wondered a bit about the front element size of some of the newer generation long lenses. The latest Nikon 600 f4 doesn't look like it is as large in the front element as the older versions. In fact, according to the data sheets, it is 6.6 inches for the new ones and 6.9 inches for the older ones. Is this because they have made the actual front element smaller? In order to do so, they must either change the focal length or the maximum aperture... It used to be that Nikon (and Canon I assume, though I'm not as familiar with their products) produced their super telephotos very close to the published specs, while Tamron, for example, produced a 280 mm instead of a 300 mm. This put them within legal tolerances for their product labeling, but also reduced the size, and presumably expense, of their lenses. In my irrelevant musings, I've wondered whether Nikon has made a similar adjustment in their latest 600. Since I've never touched one of these lenses and am not likely to, I'm free to wonder unfettered by details like the actual size of the lenses, which may not have changed in any real fashion.
Random thoughts from my troubled mind...