In title theory or mortgage states title is held in the lender’s name until the final payment is made, when title is passed or re-conveyed to the borrower.
In lien theory states, title to the property is held in the name of the borrower with a security interest or lien to the property being granted to the lender. If the property is sold, typically, the lien would be paid off and released. That process is taken care of by the title company.
In addition to the manner in which title is held to the property, there are differences in the way foreclosures are handled. In title theory states, where ownership to the property is held by the lender, foreclosures are a judicial process that involves an expensive lawsuit and might take months or years to resolve. In Lien Theory states, the foreclosure process is non-judicial and handled by a trustee.
The red states are lien theory states while the blues are title theory.