You
would have to ask a question about Kanger model numbers!

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Kanger seems to really like the alphanumeric combination, "KR808." They use it in close to a dozen of their model numbers. And suppliers and we ECFers add to the confusion, abbreviating "KR808D-1" in various ways: KR808D , KR808, 808, or even Kr8. [I'm afraid that I am largely to blame for that last one.

]
Actually, I see no mention of KR808c (with or without the parentheses surrounding 'c') on the szkanger.com website. The Kanger section of Alibaba does show a "KR808CP" [and a couple other Kanger-related sites as "KR808C(P)] with the same picture you included in your question. And, as you say, it is described as a manual switch disposable cartomizer unit, the same length as their KR208K: 124.5 mm. That is longer than the regular battery Kr8's 117 mm and shorter than the XL's 137 mm.
So, is it compatible with the KR808D-
1 (that we all know and love)
or the KR808D-
2 (aka E9, e.g., LoongTotem, Smoke51, Vapure)? I don't know.
You may want to ask LeCig (which carries both models, calling them D-1 and D-2).
All of which may be moot. I don't know of any supplier who sells the KR808CP.