Glycerol

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Glycerol - a clear, viscous, odourless, slightly sweet, non-toxic, liquid

used e.g. as a humectant, a solvent, a sweetener, a preservative, a thickening agent

has some anti-freeze properties

has a few medical uses

Glycerol and glycerin (US) / glycerine (UK) refer to the same molecule, but glycerin is a commercial term that refers to mixes that are mostly (>95%) glycerol.

You may also see the term glycol.

Glycerol is one of many glycols; glycols are a wider chemical property/grouping, of aliphatic diols, where

aliphatic = non-aromatic

diol = alcohols with two OH functional groups

Glycols include

glycerol (E422)

propylene glycol (E1520 when used for food and E490 when used for cosmetics), somewhat similar to glycerol

ethylene glycol (used in classical antifreeze, and toxic)

Smoke machine fluids were often mostly glycerol (or other glycols, but not ethylene glycol) and water.

There appear to be newer formulations that leave less residue(verify).

Vaping liquid has a base that is often a mix of part glycerin (smoother, cloudier) and propylene glycol.