Acredito que cada uma dessas conveções possuam suas responsabilidades, claro que isso muda conforme o contexto do framework ou linguagem.
Logo abaixo deixo uma rapida explicação, que eu acredito ser a mais valida, retirada de uma pergunta no StackOverflow.
These terms can be synonymous with each other depending on context, which is why each framework or language creator is free to explicitly declare them as they see fit... think function/method/procedure or process/service, all pretty much the same thing but slight differences in different contexts.
Just going off formal English definitions:
Provider: a person or thing that provides something.
i.e. the provider does a service by controlling some process.
Service: the action of helping or doing work for someone.
i.e. the service is provided by controlling some work process.
Controller: a person or thing that directs or regulates something.
i.e. the controller directs something to provide a service.
These definitions are just listed to the explain how the developer looks at common English meanings when defining the terminology of a framework or language; it's not always one for one and the similarity in terminology actually provides the developer with a means of naming things that are very very similar but still are slightly different.
So for example, lets take AngularJS. Here the developers decided to use the term Controller to imply "HTML Controller", a Service to imply something like a "Quasi Class" since they are instantiated with the New keyword and a Provider is really a super-set of Service and Factory which is also similar. You could really program any application using any of them and really wouldn't lose anything much; though one might be a little better than another in certain context, I don't personally believe its worth the extra confusion... essentially they are all providers. The Angular people could have just defined factory, provider and service as a single term "provider" and then passed in modifiers for things like "static" and "void" like most languages and the exact same functionality could have been provided; this would have been my preference, however I've learned not to fight the conventions and terminology of the frameworks your working no matter how strongly you disagree.
Reference:
Service vs Controller vs Provider naming conventions