What is a trusted third party, and what is a trust service?

A trusted third party is an independent, trustworthy entity that ensures authenticity, integrity or confidentiality of information and transactions in security and identity systems, for example a certification authority in a PKI or an identity provider in a federation; the trust service is the IAM service that maintains the list of accepted, trustworthy IAM service providers and relying parties.

Go deeper:

• Trusted third party (Wikipedia) — the cryptographic role a CA plays between two parties.
• Trust service provider (Wikipedia) — the eIDAS term for providers of certificates and signature services.