Acoustic Treatment
Home Theater acoustic treatment is sound insulation which is mainly focused to improve the audio quality. It will affects how sound moves inside the air in the room which is important for Home theater scenario for immersive experience.
Soundproof
Home Theater Soundproof is sound isolation which is mainly focused to reduce sound transmission from the room to outside and also sound from outside room to inside the room. Soundproof is improve the sound dynamic but its very costly to achieve because even the bass energy will easily transmit through 9", it can not be achieved by anything you do on wall. Soundproof can usually only be done by construction, Not by any acoustic panels.