When rape doesn't mean rape

Are there different degrees of rape? We know that there are different degrees of murder, from first degree (an intentional, willful and premeditated murder) down to involuntary manslaughter (an unintentional death, such as from drunk driving). But can the same be done for accusations of rape?

For the record, there are already laws handling the degrees of rape, but they don’t deal with variations in intent. For instance, in some states “first-degree rape” refers to a rape by force using a deadly weapon and infliction of physical injuries, whereas “second-degree rape” doesn’t require a weapon or physical injury. There’s also first- and second-degree sexual assault, which follow the same model but are not limited to intercourse.