The short version
Deep tissue and Swedish are two settings on one dial, not two different rooms.
The room doesn't change between them, and neither does the table, the oil or the person giving the massage. What changes is how fast the hands move and how much weight goes behind them. Swedish covers ground — long strokes, a steady rhythm, the whole back in one pass. Deep tissue slows down and stays put, working into the layer underneath instead of gliding over it.
That's the whole mechanical difference, and it's smaller than the marketing around it suggests. A therapist working deep does much the same thing more slowly, with a braced forearm where a flat palm would have been, and stops the moment you say stop.
So the booking matters less than people expect. You can move the pressure at any point in the hour, which means a session that opens as broad Swedish work can go deeper on one shoulder and stay light everywhere else. What you pick at the desk sets where the hour starts, not where it has to end.