You are right and wrong at the same time. Yes, they are all Hummers, but the H1 is not a Hummer. It is a HMMWV(Humvee), which is one of the best military trucks on the planet, if not the best.
Hummer is just a collection of modified Humvees, Tahoes, and Trailblazers.
The H1 is an amazing offroad vehicle. It may be slow, have loose steering, and weak brakes, but it can go almost anywhere. The other Hummers do not have that capability.
The H1 is purpose built, dedicated to being the most stable and capable offroad vehicle out there. The other hummers are built on SUVs that are meant for the road, which are not suited very well for anything guy carrying people. They do not have much of a capability besides that.
Hummer is not alone though. The new jeeps like the compass and patriot are not considered jeeps by most people.
Most jeeps are purpose built. The Wrangler, Cherokee, Grand Cherokee, and Commache were all purpose built, and were decent vehicles. The H-2 and H-3 are not exactly good vehicles, they perform poorly in nearly every way.