What is the relationship between the .lib files?

For the cache file:

Apparently you have made a new library in your project.

Euhm, no.
If you want to use that library in your project, you have to add the library to your project, and KiCad saves that setting in the sym-lib-table file. Result is that if you delete the sym-lib-table file from your project, then KiCad does not see the project specific libraries anymore.

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