The difference between an assumable mortgage and subject-to, and when FHA and VA loans are worth chasing.
An assumable mortgage is taken over with the lender's approval. You become the borrower, keeping the same rate and remaining term.
In the US mainly FHA, VA and USDA loans. Conventional loans rarely are. You go through a shortened approval with the existing lender.
You inherit the old rate, but you must fund the gap between the sale price and the remaining balance yourself, with cash, a seller note or a second loan.
In an assumption the lender knows and you are legally the borrower; in subject-to they do not. Assumptions take longer but carry far less risk.
Ask for the exact balance, rate, remaining term and any arrears, then underwrite your cashflow on those numbers instead of today's market rate.
In short
An assumable loan gives you the old rate without due-on-sale risk, in exchange for a longer approval and a larger cash gap.
Data from public sources and licensed feeds. Not investment advice.