Marriott uses nights to determine your elite status.
10 - Silver
50 - Gold
75 - Platinum

The "stays" you refer to are usually used in promotions such as the MegaBonus.

If the promotion says "earn 5000 points for every 2 stays up to 35000 points" then to achieve that it would be better to do short 1 night stays. However, if a promotion says earn 35000 points after 20 nights then it doesn't matter if you do 20 nights in one reservation or 20 separate one night reservations.