Ripping chain is used on a saw for milling. It is to cut a long lenthwise to make lumber out of, and produces fine dust instead of big wood chips from normal cross cutting.
Full comp is standard chain, where there a right cutter, tie strap, left cutter, tie strap, right cutter, tie strap, left cutter, etc
Skip chain can vary (half skip, etc) but usually full skip has two tie straps in between the cutters. It is typically used on long bars when chip clearance is a problem. It can also be used on smaller saws that run longer bars, so the saw has the power to carry the longer chain.
Full chisel is either round or square and the side of the cutter is 90 degrees to the top plate. This is the fastest cuttig chain, but it very prone to being dulled by dirt, sand rocks, etc.
Semi chisel has a rounded radius between the side plate and top plate. It is commonly used in dirty cutting conditions. It holds an edge a lot better it dirtier woods. It is just not as fast as full chisel.
Hope that helps, there are other types of chain, but those are the most common and general descriptions in my own words.