Yes! All of that deserves to be a long form. 😂

So let me see if I got this. Solo CKPool is a pool in the sense that all the miners that point to it are using its resources in terms of the stratum server and template creation. But they still get the block reward (minus pool fees).

We refer to that as lottery mining to distinguish it from what solo mining is, for example, with DATUM, where everything is controlled by you. You run the stratum server and create the templates.