Almost correct.
Your roster can be 53 only. But out of the 53 guys, every week you designate a GAME DAY roster you plan to use on the upcoming game.
The game day roster is set at 45 guys out of your 53. The other 8 guys are inactive and are not on the sideline during the game. Prior to this year, your 46th guy was a 3rd string "emergency QB." I'll explain more here:
Until last year, you could carry 45 guys and ONE MORE QB that served as an emergency QB. However, if your starter is hurt and the 2nd QB gets hurt, and therefore you put the 3rd QB into the game prior to the 4th quarter, then neither the 1st QB nor the 2nd QB could re-enter the game. You'd have to stick out the game with your 3rd QB the whole way to the end of that game.
This year, with the new CBA deal, they removed the strict rules and said "Look, you can have 46 guys and that 46th guy can be whomever you want. Even if it's a 3rd QB, the old rules for him no longer apply."
Hope that makes sense.