(Like the F-22 and F-35 do) The Shuttle did aerodynamic braking, which is sort of like using the whole vehicle as a parachute, which reduced the speed at which it had to resort to its chute, enabling the chute to be much smaller than it would otherwise have been:

https://en.wikipedia.org/wiki/Aerobraking#Aerodynamic_brakin...

But even if it didn't do that, it would need a much smaller chute than a capsule of the same weight because gliding greatly increases distance traveled through the atmosphere, which enables the vehicle to bleed off a lot more kinetic energy as drag.