Usage patterns
〈場所〉から〈場所〉までの距離the distance from one place to another
The distance from Tokyo to Osaka is about 500 kilometers.
距離を測るto measure the distance
We measured the distance between the two points with a laser.
距離が近いto be close in distance
This shop is close in distance from the station, so it's convenient.
距離が縮まるfor the gap (emotional/relational) to narrow
As they talked again and again, the distance between them narrowed.
Expressions
距離を取るkeep one's distance; distance oneself; maintain a distance 距離を置くdistance oneself; keep at a distance; maintain a distance 距離を詰めるshorten the distance; close the gap; get closer