Flite,
I really can't find a definitive answer for you except this one:
When in doubt, clarify with the controller.
To be honest, In the radar facilites I've worked at, we controllers would probably not notice nor care which you were navigating to. When you reach the boundry of my airspace, I'm going to vector you for a sequence. Happens here all the time late night when Center stops assigning the STARs and starts sending the arrivals direct. Some are heading towards the VORTAC and some to the airport. Matters not, they'll normally get a vector before they get within 20 miles of either.
Now, in a NON-RADAR environment, it's a whole 'nother story, and the controller ought to be a bit more precise with his/her clearances. And in fact, as you approach the airport, I imagine you will find that they will re-clear you in a more precise manner, unless you're the only aircraft in the area and are expecting a visual approach...
