The key difference between alignment theory and other exercise/stretching practises (yoga, pilates, etc.) is that alignment not only focuses on where your body is in space, but also evaluates the position of your parts relative to your other parts. Like when we evaluate someone's spine, we also look at the ribs and pelvis and legs. Or when we look at someone's feet, we also have to look at their knees and pelvis and torso...and also shoulders...and the head. The body is really one unit that depends on all its parts to work together properly. You'll never get to the root cause of problems if you don't look at all parts of the body. Cervical disk degeneration can originate in the foot and calf, and if you aren't looking at the body as a whole, you're going to miss the root cause of the problem.
Take this shoulder stretch. In the first picture, sure, my arm is on the door frame and my body is going past the door frame. But in actuality, I'm NOT stretching my shoulder. I'm just collapsing through the back to make it look like I'm stretching my shoulder. There isn't much regard for the position of the upper arm relative to the actual shoulder joint, and the fact that half my back is displaced is a big clue that this stretch isn't doing what it's supposed to.
In this second picture, you can see that my shoulder blade is stabilized, and I'm not allowing my body to hinge in the center to allow my arm to come back further than it actually can. Here I am actually opening the shoulder joint and getting a good stretch. It might not seem like a big difference, but if someone is supposed to be doing physio for their shoulder (to heal an injury or something) and they're doing the stretch by collapsing their back instead of just moving the arm, they're not going to get the results they could get if they did the stretch properly. It's the difference between a full recovery and a life long "bad shoulder". This applies to every stretch you do. The position of other parts, besides the part you're stretching, can make a difference to what you're actually doing, vs. what you look like you're doing.
Ok, ok, so what. It looks like I'm stretching, but really I'm not. Call an ambulance, right? Well, this concept can actually be applied to a much more dangerous situation. An example of this is when people are told they are swaybacked when really they are thrusting their ribs into the air to make it look like they are swaybacked. That's because the diagnosis is often made looking only at the the spine, ignoring the position of the ribs relative to the spine, and the pelvis relative to the spine, and the position of the femurs relative to the pelvis. Even the way you carry your weight (either on the front of your foot vs. the heel) can add to the illusion and make things appear like something they're not.
So you go to a doctor or a physiotherapist who gives you the wrong diagnosis because they miss this critical concept of evaluating your parts (spine) to your other parts (pelvis, ribs). With this wrong diagnosis comes the wrong advice to fix the problem. Usually a "sway backed" person will be told to tuck their pelvis under to decrease the amount of curve. When you tuck your pelvis you can expect a drastic decline in the health of your knees, hips, and feet. You can start stocking up on adult diapers now, because you're going to end up with pelvic floor disorder. You can expect your back pain that sent you to the doctor in the first place to stick around (oh cool!) because you HAVEN'T FIXED THE PROBLEM, which is a rib thrust. The scariest part is that thrusting your ribs out/up is asking cardiovascular disease to be your bff 4 evr. So you think you've taken care of this problem, but really you still have the problem and you've created even more problems to keep your other problem company. Now THAT'S a problem. :(
It's really important to understand the difference between the way things look or seem and the way things are. It's like katy says about fixing a flower pot on a crooked table. The flowers on the crooked stand LOOK crooked, but really it's the table that's the problem. Until you fix the crooked table, nothing you do with the flowers is going to help. So if you have a bad back, it's time you started looking at other parts of your body to fix the problem. You're not Astar the robot with all these separate functioning parts. You are one unit, and what you do with one part affects all the others.