A residential mortgage is a mortgage for a property in which you intend to live. Usually, you will have a lower deposit and higher monthly payment. You are not allowed to rent it out, or you are in breach of your mortgage contract. If you wish to turn it into a let-to-buy, you must talk to your residential lender or remortgage.
A buy-to-let mortgage is taken out with the sole intention of renting out to others. With a higher downpayment, less regulation, and an interest-only repayment plan, most buy-to-let mortgages focus on maximising profit through rental, not paying off the entire mortgage as quickly as possible.