There are libraries where label differs from library name. I suppose it matches in cases where label has only 1 library.
For example (from my subscr. list) War & Audio, Space Tones, Earth Tones, Law & Audio, Gore & Auidio and some others are all libraries of Extreme Music label.
Here is an structure example of AMP music libraries. Suffix means certain library while “parent” group i suppose can be a label or publisher.
https://www.apmmusic.com/libraries