I don't think that the Linux perspective is very special.
You are talking about
chkconfig which a utility used on Fedora, Red Hat, CentOS and similar distributions, mostly used to configure whether a particular "service" will be launched during machine booting or not.
What they call a service is just several or one "daemon", which is a backgroud process, which job is usually to wait for events or requests, and process them when they arrive. They can be local user events, network requests, time based events...
The SSH server, web server, database server, cron job-scheduler, system logger, etc. are examples of such services. They normally run in the background until you shutdown the machine. Normal users can sometimes interact with them but cannot usually stop them if they are not the system administrator.
All services are processes (one or several). A process is not necessarily a "service", i.e. your web browser or email client.