distance has 5 distinct synonyms spread across 4 of its 8 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 property created by the space between two objects or points
a distant region
“I could see it in the distance”
the interval between two times
“the distance from birth to death”
a remote point in time
“if that happens it will be at some distance in the future”
keep at a distance
“we have to distance ourselves from these events in order to continue living”
go far ahead of
“He outdistanced the other runners”
Synonyms, antonyms and the broader and narrower relations for distance come from Princeton University’s WordNet. Full sources and licences.