ITIL V3 Business Service Catalogue and Technical Service Catalogue are different views of the same services
It seems Technical Service Catalogue is often misunderstood to mean a catalogue of different services from those in the Business Service Catalogue. It's not. It is a different view of the same services. ITIL SD 4.1.4 sadly refers to "supporting services, shared services" within the TSC which I think contributes to the confusion, but diagram 4.3 makes it clear - the services are the same in both, just the perspective and detail differ because of the different audiences: internal and external.
Processes, functions and composite CIs or "systems" are not services. They are the detail needed behind each service in the TSC.
Technical Service Catalogue and Business Service Catalogue are the two faces of one coin.