'Facelift' is a generic word that generally implies an operation in which extra skin is removed and the remaining skin is lifted. Every surgeon does the operation a bit differently, and the operation should be tailored to the needs of the patient. Words like 'partial', 'mini', or 'lunch-time' are often a clue that the operation is shortened and focused on quick-recovery rather than profound and durable results. It's less invasive but wouldn't necessarily cover the extent a full face lift would.