I thought the processor was just someone who processes all personal data on behalf of the controller, basically a simple substitute for some matters. But from what I read online it seems that a processor is anyone that deals with any personal data, even partial data, as part of a service provided to the controller. So it sounds like everyone that deal with personal data as part of their job is a processor, except the end users of the service. But since processors must be bound by a specific contract to deal with the needs of the controller (article 28 says "processes the personal data only on documented instructions from the controller), then I'm afraid it will soon become a huge mess with a gazillion contracts to sign.
I hope the question is clear enough. I'm basically very confused about the actual role and duties of processors in real-world scenarios.