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How does the carbon atom attached to a hydroxyl group determine an alcohol’s classification?

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Alcohols are classified based on the number of other carbon atoms attached to the specific carbon atom that is bonded to the hydroxyl group (—OH). This classification system identifies the alcohol as follows:12

Primary (1°) alcohol: The hydroxyl group is attached to a carbon atom that is bonded to only one other carbon atom.1
Secondary (2°) alcohol: The hydroxyl group is attached to a carbon atom that is bonded to two other carbon atoms.1
Tertiary (3°) alcohol: The hydroxyl group is attached to a carbon atom that is bonded to three other carbon atoms.1

Additionally, alcohols may be categorized as allylic or benzylic if the hydroxyl group is bonded to an allylic carbon (adjacent to a C=C double bond) or a benzylic carbon (next to a benzene ring), respectively.12