You pretty much have it! Medium is organized into a series of sub publications. You can publish anything you want independently of publications, but if you choose to submit an article to a publication, you can increase your readership given that many people follow publications and might see your story that way when they otherwise would not.
The trouble with the February date line is that your story would fall off our front page before it ever appeared, so we would not be able to help you much if you submitted it now.
But yes, I would love for you to submit something to us in the future, because I really enjoyed this story and I would love to see more from you.