Processes and services are very closely related.
Both are processes with many participants, sometimes complex structures and many interfaces to other topics, people and systems.
If end customers or end consumers outside the organization are involved, this is referred to as a service.
If the process is purely internal to the organization, it is referred to as a process.
So while process and service are fundamentally comparable, there are different focuses and priorities, for example with regard to usability, payments, data protection, security aspects and feedback loops.