What is the difference in meaning between 'one on one' and 'one to one'?

Answer 1

"One on one" usually implies an adversarial interaction.
For example, a "one on one Basketball game" or a "one on one interview."
It means one person is trying to do something to the other, like win a game or extract information. It is not necessarily a private encounter. A one on one game or interview can have an audience, as long as only two people are participating in the event.

"One to one" implies a more intimate encounter between two people.
It usually, but not always, implies a private message or encounter.
For example, your boss might say "I want to have a one to one talk with you about your job performance." Or your lover might say "Let's go somewhere private for a one to one moment."