c. 1300, distaunce, "a dispute or controversy, civil strife, rebellion;" early 14c., "disagreement, discord, strife;" from Old French destance "discord, quarrel" (13c.), with later senses directly from Latin distantia "a standing apart," from distantem (nominative distans) "standing apart, separate, distant," present participle of distare "stand apart," from dis- "apart, off" (see dis-) + stare "to stand," from PIE root *sta- "to stand, make or be firm."
Meaning "remoteness of space, extent of space between two objects or places" is from late 14c. Also "an interval of time" (late 14c., originally distaunce of times). Meaning "remote part of a field of vision" is by 1813. The figurative sense of "aloofness, remoteness in personal intercourse" (1590s) is the same as in stand-offish.
At a distance "far away" is from 1650s. Phrase go the distance (1930s) seems to be originally from the prize ring, where the word meant "scheduled length of a bout." But it also was a term in 19c. horse-racing heats.