This topic has cropped up so many times.
In the UK at least you should never be told to 'fly runway heading' - there is no such standard phrase. You are told to 'climb straight ahead', 'track extended centreline' or 'fly heading xxx'.
Most of the time it is used to provide separation from traffic being vectored downwind and therefore, as has been previuously said, in conditions of extreme crosswind, the difference between track and heading is very important.