TER General Board
In my areas of operation on the east coast, I think that what we call "AAMP" (Apartment Asian Massage Parlor) is the pretty much the same as the west coast K-org apartments. I have never seen the use of KAMP (Korean apartment ...) or AKMP (Apartment Korean ...?). They are all just AAMP.
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I mostly agree with your description of "regular" AMPs and KMPs. There are fewer and fewer storefront parlors these days (see spas, below). Most of the places you describe are converted commercial space, lofts or apartments. You can still book a specific hostess but you don't have the ambiance of a fully furnished 1- or 2-bedroom apartment. As you say: common showers, etc. .... but still an enjoyable experience for me!! I should add that, at least in NYC and Boston, the AMPs and KMPs are diversifying with other nationalities: Thai, Japanese, Latina, (and I'm even thinking of an English-Bermudian!).
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In urban NYC and Boston there are also Asian spas / massage parlors that are real commercial business-y spas that SOMETIMES offer extra services. I have not tried any yet.
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For the OP and others, I think it's helpful to discuss these regional differences in nomenclature and practices (that is mostly used here on the boards). I mean, if I was going to Chicago or Houston, I would seek advice on those boards and hope to make sure I'm describing things in a way that the locals can understand and to help me. On a board, we can clarify "Do you mean private apartments or storefronts?" with more discussion and get to know that area before dipping out toes -- or other parts -- into the waters -- or other parts! 
Well I heard k-org on TER as well. TBH, I don’t talk about anything escorting IRL. But I find it odd to call them KAMP. My experience with AMPs is places that are set up like a massage pallor. They have multiple rooms, common showers, and you can book an appointment and get whatever lady is available. The K-orgs I have dealt with have apartments and you’re always booking a specific lady. Mind you, they have multiple apartments in the same building. But these apartments are mixed in with residents who are not escorts. But hey, I’m no expert. My experience is limited with K-orgs and AMPs.