In the UK, if you are instructed to fly 'Runway Heading', and do so, you have correctly complied with your clearance, irrespective of any drift. The trouble is, IMHO, that some ATCOs use the term rather loosely, and in reality expect you to track the extended runway centre line! With "After departure climb straight ahead" there should be no ambiguity. Next time you're given "Runway Heading", especially if there's any significant cross-wind, I suggest you query it with ATC.