Well, yeah... And I don't need the same gear strolling through the mall that I do on an overnight hike in the Appalachians. But walking is walking, and that's all there is to it. Mastery of the basics - breathing patterns, correct hip and heel-toe movement, a steady pace, and being properly prepared for conditions - still comes into play no matter what kind of walking you're doing.
In this way, there are no "different kinds of diving," which is simply an excuse for many people to dive with less than optimum gear.
Imagine all of the different styles you'd have to learn - and all of the different areas of expertise you'd have to master - if you didn't standardize your gear! With one philosophy on diving, it's easy to master the basics - and always have an appropriate emergency response - if you don't allow yourself to fall into the mindset of, "different types of diving."
Those who do fall into that mindset - the "Around Here" diver (they're always saying things like, "Around Here, the water's different," or, "We dive differently Around Here," or, "That may work for someone else, and I know that the books all agree to do X, but we do Y, because they don't know what it's like to dive Around Here.") does not equal local expertise. Expertise - be it local or otherwise - is earned by doing a lot of diving and a lot of studying. The only thing the "Around Here" diver accomplishes by having the "different types of diving" mindset is segregating himself (or herself) from all "other types" of diving. That is, by subscribing to the "different types of diving" mentality, all they do is restrict themselves.
Yes, I understand that a drysuit may not be necessary on your trip to Belize... And that plainly, a speargun would be totally inappropriate in a cave. But that's GEAR, not DIVING. I would agree with you that there is different types of gear, but not different types of diving.
...Which brings us back to the point that your alternate air source should be your buddy. If you and your buddy master this basic, then it'll apply to all "kinds" of diving, and the next time you have an emergency underwater, you won't have to first stop and figure out what "kind" of diving you're doing.