Do K-Mart and K Clinic have anything in common?

…I ask mainly because the “K” in each logo looks like the same “K”. I can’t seem to find any pictures of the K Clinic logo, but you can see the K-Mart logo on its Wikipedia article.

K Clinic appears to be some kind of medical clinic, probably a worker’s compensation or accidental injury style clinic. I don’t know how widespread they are, but I’ve seen their stores in both Utah and Texas.

K-Mart is the USA-wide store chain that is desparately losing out to Wal-Mart in market share.

This may just be perception bias on my part, but both businesses seem to be on the skids every time I drive past. Untended signs, ramshackle parking lots, paint peeling from the facade, etc. I was amazed to discover recently that a K-Mart near my parents’ home is still in business, even though it rarely has any vehicles in the parking lot. And the K Clinics I pass daily never seem to have any customers. (Caveat: I mainly go past them while commuting; I see very few dental clinics or veterinary clinics with customers in those hours, so I know I can’t use the customers-in-parking-lot-while-I-drive-by metric reliably.)

My theory is that, if both businesses are in dire financial straits, and since they seem to share branding with that “K”, that they’re probably owned by the same people. Seeing that K-Mart somehow scraped together enough pocket change to purchase Sears, and that they have in the past owned OfficeMax, Borders/Waldenbooks and Payless Drugs, this theoretical arrangement would not surprise me.

What does the K Clinic do, anyhow? They could be a front for the Omaha Illuminati for all I know. Does anyone have the Straight Dope on this?