that's right.. basically stamina refers to how long your player can go without getting tired and having his effectiveness decrease.
what if we just got rid of team ratings, then you wouldn't complain about them not matching ;)
the team rating reflects the effectiveness of the team you put out there in each category...meaning a good player who was tired as heck, is not effective and thus your team rating would be lower than if he were not tired.
So, Team ratings do inform about the decrease in performance (modulated by stamina) as well as match-ups.