"One-to-one" vs. "one-on-one"

Solution 1:

One-to-one is used when you talk about transfer or communications. You may use one-to-one when you can identify a source and a destination. For eg., a one-to-one email is one sent from a single person to another, i.e., no ccs or bccs. In maths, a one-to-one mapping maps one element of a set to a unique element in a target set.

One-on-one is the correct adjective in your example. See Free dictionary. One-on-one is used when there are two people involved in mutual exchange, as happens in a meeting.

The difference is rather usage-based, but most important: Do not forget the hyphens.

Solution 2:

This might be confusing because of the similar phrases such as "man-to-man" and "heart-to-heart", which refer to an interaction, vs one-to-one, which refers to a transaction (or in the database world, a relationship).

Meanwhile "One-on-One" has a sort of domination/subordination sound to it, where one is on top of the other.

At the end of the day, when two people are having a private conversation or face off or meeting, it's a one-on-one.