I don’t see it in any top-level comment, so… in chemistry, “alcohol” just means a molecule has an -OH (hydroxyl) group. That’s an oxygen atom bonded to a hydrogen atom, and essentially those can travel together as a pair and attach to others things. It imparts some polarity (to small molecules especially) and can make a compound more soluble in water.
You can of course have multiple OH functional groups attached to a single molecule. Two is called a diol or 2-ol. There’s also triol (3-ol) but you don’t hear that outside scientific contexts. You can keep going with tetrol, pentol, and other Greek prefixes, or “poly-ol” more generally. You may even see the OH group named first, as hydroxy-(something). But not everything with hydroxls ends in “ol” (as others said, sugars like glucose). Some names are historical or come from biology instead.
Anyway, the differences in “alcohol” compounds you see in your toiletry products is, well… everything about their structures beyond the OH group!
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