I think that it depends on context including how you use these terms in your culture i.e. there are formal definitions but also slang definitions.
Formally, RESTful web-services should refer to the standards used in the implementation architecture but says nothing about the functionality provided e.g.
Does your service use SOAP or RESTful webservices?
This statement doesn't define what those web-services do, just the structure they conform to. You can find more here.
When salesforce.com talks about the REST API they're talking about an API implementation that conforms to RESTful standards. In short they're saying:
We have an API and it uses RESTful concepts in it's architecture.
The documentation for the REST API is therefore quite different.