one-on-one—(attrib.)
1. involving a direct contact between one person and another:
- Our school offers both one-on-one instruction with your own teacher and group instruction.
2. playing or fighting directly against a single opponent:
- I was quickly engaged in one-on-one combat with a tall, lean warrior apart from the central conflict.
one-to-one—
1. said of pairing each element of a set with an element of another set:
- I strongly identified with this philosophy of enhancing social skills in children by pairing them one-to-one with college students.
2. = one-on-one 2:
- The brawl began as a one-to-one fight between a black inmate and a Latino, and escalated into a small melee with up to a dozen inmates.
Note: Neither expression correlates in meaning with the phrase one by one—one after another:
- I found these group ward rounds more efficient and also more enjoyable than seeing patients one by one.