types of modeling
1.SUB DIVISION modeling

Here is a decent video describing SUBD vs POLY modeling: https://www.youtube.com/watch?v=DNOvEUkvj60

2.HARD SURFACE modeling

Hard surface describes modeling non-organic shapes like tools, appliances, and machines. These are characterized by objects with sharp (HARD) edges.

3.POLY modeling

The Video above gives a concise description but in a nutshell, SUBD starts with a relatively low poly count object that is (SUB-DIVIDED) into a higher polycount (
SMOOTHER) model. 3D-MAX does this by applying a sub-d modifier on top of a polygon cage of the model. Maya used to have to physically convert the poly model to sub-d before it could be rendered but now the smoothed model of the low poly cage can be directly rendered.

So sub-d is the act of taking a lower poly frame or cage and smoothing it by sub-dividing all the polygons in that cage. The more levels of subdivision the smoother the model.


These next two are modeling work flows and here is something describing each...
4.PLANAR modeling

https://www.youtube.com/watch?v=9F6EEQDtNSs

5.EDGE modeling

An example of edge modeling would be in modeling a human head you want to layout the edges in loops around the eyes, the mouth, the nose. So you can start with a basic poly shape without worrying about "edge flow" and then rebuild the geo on top of the basic form poly mesh such that you create loops of polygons around the features that would need to animate in a natural way like the mouth, eyes, ears, nose, etc. There are a ton of video on this site that are a great way to learn about model topology and edge flow for modeling organic shapes that need to deform in a natural way

For a simpler case look at "Holy Geometry" tut on this site, you can see a square cube with a round hole. You can see there is a circular ring of polys around the hole. That is called an "edge loop" or "face loop" and is required to get a smooth circular opening in the flat square polygonal face of the cube.

If you look at a good animatable model of a human head you will see edge loops around the features of the mouth, eyes, nose, etc. These are typically created by extruding faces on top of a polysurface that approximate to shape of the head but does not have geometry that follows the natural flow of the muscles on the face.


You left off NURBs and NURMs modeling (also called SURFACE MODELING)

These are used to model very mathematically accurate surfaces for manufacturing of real products from coffee pots to the SpaceX's Dragon space capsule.