bay has 7 distinct synonyms spread across 4 of its 10 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
an indentation of a shoreline larger than a cove but smaller than a gulf
small Mediterranean evergreen tree with small blackish berries and glossy aromatic leaves used for flavoring in cooking; also used by ancient Greeks to crown victors
a compartment on a ship between decks; often used as a hospital
“they put him in the sick bay”
a compartment in an aircraft used for some specific purpose
“he opened the bomb bay”
a horse of a moderate reddish-brown color
1 of the 10 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for bay.
Synonyms, antonyms and the broader and narrower relations for bay come from Princeton University’s WordNet. Full sources and licences.