Summary: Sound proofing and acoustic treatment are not the same. One limits the sound leaving and coming in to a room. The other changes how sound behaves within a room.
Often, people will use the above two terms interchangeably when they are in fact completely different. Here is a breakdown of the two and why they are different:
Soundproofing is the act of limiting or removing the sound that travels in or out of a room. Usually, people want to keep the noise out. There are road noises, noisy neighbors and other sound pollution from the area. However, there are situations when you want to keep the noise from going out. For a studio, using sound deadening foam to stop echoes is not enough, you also need to prevent sound from going out and disturbing everyone else. For a movie buff, it is simply about keeping the sounds of explosions and gunfire within the movie room. Stop sounds from going in or coming out by using heavy, dense building materials and blocking any air gaps in doors and windows.
Acoustic treatment is entirely for controlling the sound reflections within a room. Using acoustic foam panels, you can control the amount of audio reflection within a room. The most common use of acoustic treatment is for a professional or home studio. Soundproofing can be part of the acoustic treatment of a room, but only in situations that require it. Improving the acoustic characteristics of a room is far easier than soundproofing both ways. Acoustic treatment often involves adding elements to a room while soundproofing involves both adding and replacing such elements.