Is there any difference between actually raping a minor and just having sex with him/her, when it comes to this law, or is it "statutory rape" in both cases?
Consent, as defined by the laws in question, can not be given by a minor so it is automatically a statutory violation.
What? Of course consent can be given by a minor, rape isn't the same as sex with a minor who grants his permission. When you fuck with 15 yo with her approval it's not a rape, though it's still a crime.
PS. Well, at least that's how it works in EU, dunno about america.