A "keg" refers to the whole directory structure associated with an installation. A "bottle" is just a tarball containing that structure from a build on the CI, rather than a from-source installation.
It makes sense but, like you said, you're exhausted and don't care.
Bottles (binary installations) are an addition to Homebrew; it was originally a source-only "package" (really just Ruby scripts that downloaded tarballs and ran `make`) manager.
Terminology is important. However, the standard terminology of package management does not always map cleanly to Homebrew's behavior. If the options are inventing our own terms or using preexisting ones unlike everybody else, I'll always go with the former.
Edit: I'm mostly thinking of things like "keg" and "bottle"; "tap" could indeed be replaced with "third party/external repository", and a "formula" could be called a "package description" or something equally generic.
