A night is a night at a participating hotel. So stay 3 nights get 3 nights credited.

A stay is all consecutive nights at the same participating hotel (whether or not single or multiple bookings) - can be as short as 1 night or weeks or more. So stay 3 nights at the same hotel get 1 stay credited.

Those qualifying (or topping off qualifying) cheaply tend to do so on stays (since lower thresholds) - but depends on your circumstances. In some cities you could spend each night in a different hotel to quickly rack up stays.