Glycerin is the natural form of glycerol. That is, it is mostly glycerol, but has some other components, depending on the source and method of processing. For many commercial uses, this does not make any difference, but it can be purified to essentially pure glycerol for chemical processes.
The fats and oils which are used to make soap are esters of glycerol which are broken down by NaOH to give the sodium salt of the carboxylic acid (soap) and glycerol, which is collected as separate layer. (The different sources of fats and oils will give different impurities.) As both layers are very viscous, separating them is tedious. It is thus amusing to to have soap producers boasting “with added glycerin!” meaning less well separated. “Hand-crafted” soaps typically have most of the glycerin left in, because the backyard producers do not have the technology of the big soap makers, who can produce glycerin of sufficient purity to be sold at a modest price for food and cosmetic use.
Glycerol is also produced when making biodiesel, where methanol CH3OH is used instead of NaOH. Thus it is essentially a low value waste product from two major industrial processes, and produced in far greater amounts than commercial uses demand. Thus many end processes are essentially ways of trying to get some small value from a waste, e.g. by burning it for energy or adding it to cattle feed.