We have to start this essay with a formal position; to wit:
"Running isn't meditation."
That will immediately rub some people the wrong way because they have said it to themselves, believed it, or espoused it to non-runners as a means of justifying time spent in the act of running. Having it challenged this way probably doesn't feel good. But running is most definitely not meditation. Meditation is meditation.
Meditation, just like running, is a skill, not a byproduct. You either practice it and get better at it for whatever reason you may have, or you ignore it (at your peril, which--admittedly--is a sliding scale of risk) and keep doing what you're doing. There is certainly something to be said for the idea of moving meditation, but it just isn't the same thing. Even in combatives training, like boxing and grappling, there are people who make the mistake of thinking one is the other and vice versa. Just today, I read the following quote on social media from a wrestling gym:
"I truly feel you are working at the highest level of 'meditation' when you are going live in a sparring session."
Far be it from me to tell someone how they feel, but this person is wrong. Or, at least, their labels are. Flow? Maybe. Meditation? No. You're just doing yourself a disservice by confusing the two and, honestly, holding back your own development. Not just as an athlete, either, but as a person.
When people are running and they think they are meditating, they are either experiencing flow or some form of inattentional blindness, but neither are meditation; there are very different things happening at the neural level in each case, but the delineations can be difficult to sense. It comes down to grasping each concept in order to better understand performance at a subconscious level, but the tools we have at consciousness can be clumsy or inelegant in this regard. Calling any sport or act "meditation" simply because it brings you some measure of calm or focus doesn't make it so. That conceit is exactly what works against the value of both flow and meditation.
Can an act have a meditative quality to it? Sure, but it's probably borne of mindfulness, not meditation; the best example of this I can think of is tai chi, but it is hardly exclusive to that art, or any other for that matter. (I'm looking at you, yoga.) You can immerse yourself in the moment while you do dishes, even, performing the act with a presence of mind that places you fully there and makes the separate acts of scrub, rinse, dry, repeat meditative in execution...but that's not meditation, it's mindfulness. The latter can certainly be a gateway to the former, but they are not the same thing at all.
Meditation isn't flow, either, any more than flow is meditation. The more experience I have with flow, both as an athlete and a coach, it occurs to me that most of the people who think running (or any sporting movement) is their meditation just don't have clear definitions of what is actually going on. Cognitively, some people just don't have the precision to stop one from spilling over into the other. That's not surprising--we have one brain and only so much vocabulary to describe what we feel and how we feel it. It can make for some fumbling while working with incredibly nuanced and complex ideas.
Flow is what athletes call "being in the zone" or other such t-shirt worthy phrases. It was coined by Mihaly Csikszentmihalyi, which I am probably butchering in spelling only slightly less than I would trying to say it out loud, a psychologist with a keen grasp of the performing mind. Mihaly posited that when a person is in a fully immersed state during an activity, they will feel energized, focused, and completely engaged to the point of being one with the activity. There may even be altered time perceptions and a state of "hyper-focus." He described it as single-minded immersion, which is the sum of all your abilities being perfectly aligned with the task at hand; it's a deep and effortless fixation on the actions being taken, unencumbered by emotions or thought.
Close, but that's not meditation. In many ways, it's the opposite of it. Hyper-focus on something is not the goal of mediation and that is what flow is.
Meditation is the act of clearing one's mind--eliminating distractions, thoughts, emotions or anything else that might serve to clutter someone's state of being. The value in meditation comes not from the execution of some external action, but in the ability to focus on nothing; letting thoughts and opinions pass observed, but unacted on, in the interest of clarity. Nothingness is very clear, indeed...particularly when you don't think about it. (Good luck.)
It requires tremendous practice to meditate effectively, the changes to the brain it makes are noticeable, and the improvements to a person's life are invaluable. And it does all that for minutes a day, if you can believe it. You don't "flow" with mediation like you do with wrestling, running or any other sport. You just are.
Trying to combine the two is like tying your shoes while wearing oven mitts because you're baking cookies at the same time; it can be done, but there is definitely a better way and that way is to keep them separate and respect them as such. It becomes pretty clear that when someone says that "running is my meditation," they are actually missing the point of the latter and not harnessing the flow created in the former. That's a problem, because we want to be able to enter flow at will and that takes (a) cognition and (b) practice.
So your goal should be to demarcate the states and then create robust psychological infrastructure around each. For flow, that means figuring the perfect balance of effort and challenge. For meditation, it means being able to quiet your inner-chatter, at least insofar as interruptions are concerned, and to just be in the moment and one with the nothing. Accomplishing one of those will make you a better athlete. Accomplishing both will make you a better person.
And those are two different things as much as running and meditation are.