When a room feels stuffy it means that the room lacks fresh air. It is usually at least a little too warm and there is no perceivable air movement in the room. The first thing one wants to do upon entering a stuffy room is open the windows, or at least the door, or turn on the air conditioning. Stale air would have a similar meaning, but is usually used for places that have been sealed off for longer periods of time, as in a deep cavern or a mausoleum. A mausoleum is a grave and usually houses a person considered very important or several people (or more) from the same family and is above ground.
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