That's the short answer, but if there's one thing we've learned over the years here, it's that I can't just give short answers, so here's some rambling for ya...
Animation is an art, and what you're talking about (the principles of animation, such as arcs, overlap, path of action, etc) are the foundation of the ART behind bringing a character to life.
When you say "types" of animation, I assume you are referring to the different mediums of animation, such as CG, hand-drawn, or stop-motion. I'd even argue that performance-capture is evolving into its own medium, with its own set of challenges, nuances, and workflow necessary to turn performance capture into something that feels alive and entertaining.
All of these mediums are simply different tools that animators use to create their art. That's all they are - TOOLS. They are the means to an end for the artists, and the storyteller chooses whichever medium will best serve the story (or the producers choose whichever medium will best serve their pocketbooks, in many cases).
Do the principles of art employed by a good photographer (including lighting, shadow, angles, composition, exposure, focus, etc) change depending on their camera? Do they use their same knowledge of exposure and focus on a digital SLR vs. a traditional 35mm camera? Of course they do. They're an artist simply using different tools to tell the same story through their art, using the same exact artistic skills they've honed throughout their career.
Are there different technical details they need to learn, though? Sure there are! Each camera will work a little bit differently, the glass in the lenses will react differently to light, the functions, dials, and buttons will be placed differently, etc. However, learning the location these buttons and controls is easy compared to the years of dedicated practice and learning required to truly master photography.
Animation is exactly the same. Each medium has its own technical challenges and unique workflow, but the art - and more importantly, the principles behind that art - remain exactly the same.
Even if you only look at CG animation as an example, you could still compare it to the challenges our photographer faces when picking up a new camera. If you're newer to animation, you have maybe only learned one 3D animation program so far, and the idea of being thrown into an unfamiliar software package probably scares the pants off of you. But guess what? It's just like the cameras we discussed, and learning a new program will be nothing more than relearning the location of all the same buttons and functionality, which will essentially remain the same.
You'll need to relearn how to move your character, how to save keys, and how to edit those keys. These are software-specific methods you could learn in a matter of hours, or at worst, a few days. A trifle compared to the years necessary to master the fundamentals of animation.
Comparing mediums is very similar to comparing software packages. Each medium requires some serious dedication to learn the intricacies of that specific medium (you won't be able to do strong 2D animation until you master drawing, perspective, form, etc), but the fundamentals of the art remain exactly the same. The principles that take so much study and practice do not change between mediums.
Animation is animation, regardless of the medium or the tool. If you're new to this stuff, my advice is to choose your favorite medium, choose your favorite program/tool, and then just dive in and ignore everything else until you've mastered the ART. Then you can start fiddling around with different tools and mediums again.
The important thing as a student is that you learn the fundamentals of body mechanics and performance and storytelling. Once you have armed yourself with these skills, you can learn any medium or software package in relatively short order.