What are the benefits and differences between Apple Music Membership and Family Music Sharing?

An apple music membership give you access to millions of songs via streaming (or you can download to your device). Family music sharing lets you share music purchased on itunes with other family members.

Or are you asking about a Family Apple Music Membership vs. Family Music Sharing?

If so, in addition to have access to the millions of songs, with a Family Apple Music Membership each family member has their own library, playlists, personalized 'for you' section, etc.