(one hydrogen atom and one oxygen atom bound together)
The terms hydroxyl and hydroxide refer in a general way to
OH, i.e., a oxygen atom and a hydrogen atom bound together.
The term hydroxyl, according to context, can refer to:
the hydroxyl group aka hydroxy group - OH as a functional group, which means a specific configuration of atoms that can be a section of a larger molecule.
hydroxyl radical - neutral OH, which is reactive because its outer shell has an unpaired electron, one being paired with a hydrogen electron.
hydroxyl ion - ionic OH, typically a negative ion, i.e., anion. It has a negative charge but its stability is enhanced from what it would be, for having no unpaired electrons.
The term hydroxide, according to context, can refer to:
hydroxide ion - another name for a negative hydroxyl ion.
any compound that contains a hydroxyl group, such as sodium hydroxide (NaOH) or ammonium hydroxide (NH4OH).