care has 20 distinct synonyms spread across 9 of its 11 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.
the work of providing treatment for or attending to someone or something
“no medical care was required”
judiciousness in avoiding harm or danger
“he exercised caution in opening the door”
a cause for feeling concern
“his major care was the illness of his wife”
attention and management implying responsibility for safety
“he is in the care of a bodyguard”
activity involved in maintaining something in good working order
“he wrote the manual on car care”
feel concern or interest
“I really care about my work”
be in charge of, act on, or dispose of
“I can deal with this crew of workers”
Synonyms, antonyms and the broader and narrower relations for care come from Princeton University’s WordNet. Full sources and licences.