This one should be simple but it comes up time and time again.
It may not be in the UK phraseology book but runway heading is a heading - point the aircraft in that direction.
Straight ahead is a line you can draw on the map ectending the runway centreline - it's a track to make good. As a controller I do not concern myself greatly with how the pilot may fly that track but I am fully aware of TRK mode in modern aircraft and I know that if the runway has an ILS the localiser back-beam may be a bit of a help.
I guess the problem arises because controllers often use the two terms interchangably when it makes little difference (i.e. little wind or when it's just to get the aircraft going in a general direction) - and in these circumstances I'm not going to know whether he instruction was correctly interpreted and implemented or not. But I do use the terms correctly (OK I admit it, I know I'm not supposed to but do sometimes say runway heading), and when it matters I hope and expect that pilots understand what the clearance means.
Of course speke is right, if you are unclear what a clearance requires you should ask, but for me there is nothing ambiguous about the two phrases.