Multiplicity of mind. The idea that a mind is normally many rather than exceptionally many is much older than IFS — William James, Gestalt, ego-state work, schema therapy and Hubert Hermans' dialogical self all got there independently. IFS's contribution was not realizing it, more the way of being with the parts: a repeatable way of meeting them once you've noticed them, treating them with respect and curiosity.
Systems thinking. Schwartz trained as a family therapist, and it shows in the load-bearing places. Parts get treated as members of a system with roles, alliances and stalemates, which is why the move is almost never to remove one. Take a member out of a family system and the system reassigns the job.
Witnessing consciousness. The Self of IFS is close kin to what contemplative traditions call witnessing awareness, and the resemblance isn't accidental. This is a strand we find very interesting, so the glossary goes further into Metta Bhavana (Loving-kindness Meditation), the Brahmaviharas, and where we think the contemplative framing helps and where it becomes a way of avoiding things.