Question about Deeds of Trust

I live in a Lien-Theory state. When a property changes ownership, even if it is financed, the new owner’s deed (bearing their name) is recorded in the land records along with the fact that they have a mortgage to purchase the property.

Now, my question: In a Deed of Trust state, the lender owns the property until the debt is satisfied. If the seller is financing the property for the buyer, how is the buyer’s ownership interest in the property recorded?

Any help is appreciated.

A deed of trust is an arrangement among three parties: the borrower, the lender, and an impartial trustee. In exchange for a loan of money from the lender, the borrower places legal title to real property in the hands of the trustee who holds it for the benefit of the lender, named in the deed as the beneficiary. The borrower retains equitable title to, and possession of, the property.

The recorder’s office lists the property as owned by the borrower and records the deed of trust with the borrower as grantor.