ATC should never ask you to maintain runway heading.
You maintain levels.
You continue on headings.
I think this has been covered before, but:-
1. Continue on R/W heading implies fly the published runway QDR.
2. Climb straight ahead implies the same as 'track extended R/W centre-line'.
I could be wrong though.
Many years ago, the TWR controller (non-radar) at my local airport would issue climb 'straight ahead' clearances to separate IFR and SVFR traffic. However, the instruction always originated from a radar environment, that is it was passed on behalf of the approach, or (occasionally) area radar controller.