Which of the following transactions is a recharacterization? All transactions were made during $2023.$

A direct transfer of a $2023$ traditional IRA contribution to a different traditional IRA with the same trustee.

A direct transfer of the entire balance of a traditional IRA, including contributions made in prior years, to a Roth IRA.

A trustee$-$to$-$trustee transfer of a $2023$ contribution plus earnings on the contribution from one type of IRA to another type of IRA.

A trustee$-$to$-$trustee transfer of a $401($k$)$ to a Roth IRA.