There are two basic types of cuts, rips and crosscuts. Rips go with the grain and crosscuts go across the grain. Think of the fibrous nature of wood as a stack of tiny straws. A rip blade's teeth tend to have a flat top and deep gullet (the notch between the teeth) as the saw chisles out the wood in longer chunks. A crosscut blade has teeth with an angled top to cut thru the fibers of the wood. Half the teeth are angled one way and half the other. Crosscutting produces finer sawdust than ripping.
A combination blade has some teeth of each type. Necessairily it will be a compromise between ripping and crosscutting. Cheap combo blades do neither well. A good combo blade will do a good job of both, but for finest results you would want dedicated blades for both types of cuts. Using a rip blade for cross cutting will produce a very rough cut as the fibers are torn from the wood instead of being cut free.
A grove cut into the surface of wood (but not completely thru the wood) is called a dado. These are made with a TS and multiple passes with a single blade or with one pass with a dado blade. They are also made with routers. One variation on this that is used is the stopped dado. This is like a conventional dado but does not extend to the edge of the wood. This is used on shelving and the like where you wouldn't want to see the notch. You normally cut stopped dado's with a router.
If the same type of cut is made on the edge of the board it is called a rabbet instead of a dado. The same tools, and others can create this type of cut.
TS's are used for ripping and crosscutting
RAS's are primarily for cross cutting
CMS's and SCMS's are used for cross cutting
Routers are used for rabbeting and dadoing
A Mortise & Tenon is a special type of wood joint where a rectangular hole is cut in one piece of wood and a tongue of similar dimension is cut on another. Tab A fits in Slot B and makes a very strong joint. If the mortise goes completely thru the stock it is called a through mortise. If it doesn't penetrate the wood completely it is called a blind mortise. You normally have a mortising jig to cut the mortises and a tennoning jig to cut the shoulders of the tenon.
You also have finger joints and dovetail joints. These joints are used when attaching wood at a 90° angle. The dovetail is very strong and resists pull out and is used in applications like door fronts. Doevtails can be visible from both sides (through dovetail) or only visible from the side (half-blind dovetail) There are some exotic variations on this (double-double, etc). Finger joints are also called box joints. They are similar to dovetails but have a square profile instead of being angled. Box joints are normally visible from both sides. Dovetails and box joints can be cut in a variety of ways, with a TS with a regular blade, on a TS with a dado blade, with a router and by hand.
Other joints are made with biscuits, dowels and other fastening methods.
Mark has given you a very good overview of the basic cuts. There is one ome that is a special case of the rip cut. That is the resaw. With this you use a band saw for the most useful version. You cut thin slabs off the face of a board. This done on a fine expensive hardwood will allow you to glue them to a substrate of a less expensive wood and have a high quality shop made hardwood plywood.
There are lots of books and Mag's that can give you the basics of woodworking. My personal favorite is Fine Woodworking. http://www.taunton.com/fw/. Taunton press has most of the good woodworking books you can find. There are lots of other mags that are much more project directed.
One warning, This thing you are starting (woodworking) may just take over a large part of your life. I am not a working Professional woodworker, but I want to be. I have been cutting wood off and on for the last 40 years right after my Jr High shop class. I bought my 1st table saw while I was still in school becoming an Engineer. I work in the computer world. And right now I should be putting together a presentation to sell our latest box at $4M each, but instead I am answering questions about woodworking. You can tell where my heart is.
I have lots of good information, tips, plans, pictorials of techniques, etc. all online. While you're there order yourself a Rockler catalog so you can get all of the odd little bits and pieces that woodworkers need. I'll also make 50¢ on the deal!