It's quite simple: Services need to be switched on (by you) for each client who gets that service. Automatic Services are switched on for your clients automatically.
Services most often represent the services that you sell in your practice.
On the other hand, Automatic Services do the day-to-day admin in your practice, such as taking on new customers or sending Christmas greetings.
Other than that difference, Services and Automatic Services are the same – they contain one or more Jobs... those Jobs contain Tasks... and so on.
If you don't want all clients to get an automatic service
Having Automatic Services running for every client may not be suitable, so you can decide which clients the Automatic Service should be applicable to. You can add filters to limit the matching clients. For example, you might want onboarding to only happen for current clients, not prospects or former clients. You might want to limit Automatic Services by client size, industry, or anything else you choose.