That is a little confusing.
Home Sharing and Family Sharing are 2 different things, and show very different things.
Home Sharing shows iTunes libraries from computers (only computers) on the same network as the device being used to view it, that are Home Shared using the same Apple ID. The library can include downloaded purchased music from iTunes, or obtained from other sources such as CDs, but not Apple Music subscription music.
It will not share content from iOS devices. Only iTunes Libraries from computers, Macs or PCs.
Family Sharing will share purchases from iTunes only, to all Apple IDs that are part of the family group. It will not share any content that was not purchased from iTunes and will share an Apple Music Family Subscription, but will not automatically share downloads from the Apple Music subscription service.
On an Apple TV, you access Home Shared library content through the Computers App, and Family Shared purchases through the Movies, TV shows and Music apps.
Home Sharing uses a single Apple ID to share libraries on the same network, while Family Sharing can be used with up to 6 Apple IDs sharing their purchases, but does not require they be on the same network.
See here: Share App Store, iTunes Store, and Apple Books purchases with Family Sharing - Apple Support
and here: Use Home Sharing to share media from a computer to other devices - Apple Support