Not entirely.
Payment by instalments (AmEng installments) is a way of buying something by making a series of small payments (usually weekly or monthly) to the seller. The size and number of instalments is agreed at the beginning, the item is handed over, and the buyer uses the item. Depending on the terms of the purchase, the item may legally belong to the buyer after the first instalment, or it may legally still belong to the seller until the last instalment is paid (hire purchase).
The 'item' could be a loan - these can often be paid off by instalments.
A monthly payment is any regular payment made every month. Examples of monthly payments which are not instalments:
- Mortgage - I don't pay monthly to the seller, but to the bank.
- Car lease purchase - I pay the seller regularly but I don't own the vehicle on making the final payment: there is a separate, optional 'buy out' payment after that.
- Regular payment plans for dentistry or electricity - I pay for what I use, averaged over time; sometimes I have paid more than I have used, sometimes I have used more than I have paid. From time to time the payments change.