Question:

Why there might be a difference between library search results and the filter facet count for non-Vault-Owner profiles?

Answer:

Vault Owners do not have any security applied to their searches, so no checks are done to determine which documents they have access to, or which version of the documents are the latest visible to them. This means that when a Vault Owner does a search, they are only ever seeing the absolute latest version of a document. If the prior version of a document matches a Vault Owner's search criteria, it will never get returned.

Any user that goes through security/sharing settings, may have a configuration where they have more than one role on a document, and they are assigned to those roles via multiple groups. This can create conflicting results between the latest versions they can see. 

Related Documentation:

Vault Help Documentation: N/A