There's really no such thing as a PhD in General Theoretical Physics. A PhD is basically about becoming the worlds foremost expert on a single, tiny little topic. The phrase "theoretical physicist" has taken on a bit of colloquial definition that isn't quite true. People like to equate it with things like string theory, the multiverse, black holes, or the "Theory of Everything." Truth is, there aren't really many physicists (either theoretical or experimental) that are 'working on' the ToE. They're working on topics that may pertain to such a ToE in a very big way, but their specific research topic isn't going to be "The Theory of Everything."
Theoretical physics constitutes the theoretical perspectives of any branch of physics you could name. In any branch of physics, there are theorists and experimentalists. Some fields have considerably more experimentalists, and some fields have more theorists. In some fields, there's really very little distinction between the two. It really just depends.
On a side note, you're still in high school. It's far too early to be committing yourself to a PhD in physics. It's good to have big goals, but you haven't yet really been exposed to physics in any real capacity. Make sure to keep your options open, and get as much math done as you possibly can.