Does doing yoga and stretching have an effect on how your body looks? Like does someone who is SUPER flexible look different than someone who has super tight muscles?
Here's a quick example: someone may exercise a lot, including resistance training, be really strong, but not practice mobility or flexibility training. This may cause their anterior muscles (anterior delts, pectorals, abdominals, etc) to be tight, pulling their shoulders forward giving them a slight kyphosis (hunchback). This gives them the hunched forward look with bad posture. Now, strengthening the muscles of the mid and upper back will help bring the shoulders back but if the flexibility is lacking then the shoulders will still pull forward and posture will still be poor.
Also, don't forget that doing exercises through their full range of motion works wonders to increase flexibility as well. Eg: squatting takes your leg muscles through a range of motion not generally seen in day to day life.
I consider there to be 4 main pillars to health and fitness: cardiovascular health, strength, balance and coordination, and flexibility. You should incorporate all 4 pillars into your workouts and training for optimal health!