We're just a poor fellas who don't know what to do, of course. However I remember seeing an "explanatory"
local ATS leaflet regarding just this. I.E. the difference between instructions
continue straight-ahead and
fly runway heading.
From my point of view a heading is exactly what it is, a datum relating to imaginary direction up north and airplane's longitudinal axis.
ATC know what they want and 99% of the time they say exactly so. Among other issues, it's the iceberg of the 1% that makes flying so darn complex as it is.