Most people that I know who run refer to themselves as runners and would feel slighted for anyone to refer to what they do as merely jogging. Similarly anyone who actively maintains a yoga practice would be offended should someone refer to their activity as simply stretching. With this comparison made there is no question there is a difference between Stretching and Yoga.
I am sure many runners can relate to this scene….you finish your run with your running friends or running group and some of you might go to the nearest curb and start stretching your calves out or against the nearest wall, or maybe even hold onto the nearest wall and proceed to stretch your quads, often maintaining full conversation with your running comrades. Depending on where you are at, some might even go to the ground or floor and do some other common stretches that focus on the hip flexors, calves, quads and hamstrings. Most people will fly through several stretches within a short amount of time and whenever there is a group involved, the talking most likely continues. I would guess that most people have the same objective in mind when they stretch and that is to lengthen the muscles that were involved with running as running shortens them. There are no issues with this objective and for some people (limited small percentage) this typical stretching routine might be all that is needed to avoid injury but for most others it is not sufficient or does not give you the full potential of your performance capability.
Let’s take an example…tight hip flexors from running. If you were just going to stretch out the hip flexors, most likely you would do pigeon pose, butterfly or cobbler’s pose and/or any figure 4 variation. Over time you might experience a release in your hip flexors from doing these poses as stretches but it is unlikely you are going to really make a long term impact unless you take a more global view of your body. For your hip flexors might have become tight due to issues elsewhere in the body, such as your arches of your feet, your calves or even hamstrings and by practicing a holistic form of yoga will most likely address multiple areas of the body and not only provide relief to your hip flexors but also address other areas of the body through strength and balance work.
So although stretching is a component of yoga, yoga goes well behind this single and narrow focus to combine increasing flexibility (stretching), with balance and strength through a mind-body connection that is united through breath work. Now not every yoga pose or even every yoga class addresses all holistic angles but within many yoga classes you do get more comprehensive conditioning that brings all elements into play and ultimately benefits your overall running performance.