To address the last question, "Cataloging" is the process of informing the Store about the physical discs you own in order to get access to digital offers in the Store. This will happen automatically for Premiere systems connected to the Store because these are disc based systems (but obviously can still download SD and HD Store content) whereas the Terra/Strato systems, being digital based, require proof that specific content is owned on disc before the Store will present an available digital offer. This is why we "Catalog" for Terra/Strato systems.
"Verifying" is the process of proving ownership of a physical disc to allow the content to be played back from a digital copy stored in a Premiere system. This requirement was a negotiated contract term with the content owners in exchange for allowing a persistent copy of Blu-ray discs to be written to K's Premiere servers. Owner's have two options for playback of BR content stored in a Premiere server, place the physical disc into a BR capable player (content still plays from the server, not the disc), or place the disc(s) into a Vault. Both of these are "verifying" ownership of the disc. The Vaults were created to import, store, and "verify" ownership prior to BR playback, and to eliminate the need to place the disc in an optical drive each time a BR movie is played back. In addition, the Vaults will occasionally run the inventory mentioned above to verify the physical disc are still present in the Vault (haven't been physically removed by opening the Vault). There are other things that can trigger an inventory check, separate from the one conducted periodically, and these are all related to "verifying."
The two, although separate, are related in Premiere systems because the process of "verifying" also proves ownership that allows for digital offers, (effectively "cataloging").
Jim