marble:

For Sub-D (subdivision) we are talking about both DS, and VWD. Sub-D is the algorithms used (Catmull-Clark, Cat-Mark, Loop, Gérald-VWD), and tessellation is the way polygons (whether quadrangles, or triangles) are formed on a mesh. Example would be Catmull-Clark yields all quad sub-d, while Loop yields all tris sub-d. Gérald's own sub-d algorthim yields a tri-mesh which if from quads the tessellation will be like the one in the image below:

The image above also serves as the second answer to your questions (Springs). That is a mock-up for the Mass/Spring model for cloth simulation. Basically "springs" are what allow cloth to bend and fold, but much more is involved. There are many different types of springs that could be utilized within a simulation such as Torsion, Tension, Damping, Bend, Shearing, Structural, Edge, and etc. You really don't need to concern yourself with these, but just know that springs are what allow the cloth to work as, well, cloth (same goes for hair).

For the image above, imagine that every edge you see is a spring. But, note, springs can even be invisible attached to the visible structural springs. So, just because the mesh is a limited tessellation, the spring count can be high based on what springs are actually being created at sim time.

Here is another example of tessellation for cloth simulation. This is a Sub-D Isotropic tessellation:

I hope this helps...

• EDIT: I was writing when Gérald posted above, so just consider this an add on to his post. He answered what was needed.