Yes, based on the stamina of the player, how many minutes he's playing, the style of defense, offensive tempo and stoppages in the game, players can get tired which can impact performance. There is no game to game fatigue – meaning everyone starts every game at 100%. The stamina ratings refer to their in-game conditioning. For example, playing a player with a 20 stamina rating for 35 minutes is not a good idea – he’ll stay in the game, but he’ll be tired and play worse.
Durability refers to their likelihood of injury and if they do get injured, how quickly they can recover.