PROCEDURES FOR AIR NAVIGATION SERVICES AIRCRAFT OPERATIONS (PANS-OPS, DOC 8168)
The following is taken from
ICAO Doc 444 ‘Air Traffic Management’ Chap 12-9
“a) [AFTER DEPARTURE] TURN RIGHT (or LEFT) HEADING (three digits) (or CONTINUE RUNWAY HEADING) (or TRACK EXTENDED CENTRE LINE) TO (level or significant point) [(other instructions as required)];”
Chap 12-17
... heading to be followed “CONTINUE RUNWAY HEADING (instructions);
... when a specific track is to be followed TRACK EXTENDED CENTRE LINE (instructions);”
From this, ‘Heading’ means fly heading i.e. aircraft reference.
‘Straight Ahead’ appears to be a corruption of “Track Extended Centerline”, thus it means fly track.
If you do not know the difference between heading and track then you should not be flying.