In the UK, the term 'Climb straight ahead' is also used by ATC.
This means that you must follow the runway centreline and adjust for wind.
In the past, a couple degrees of drift didn't make much difference to ATC. However, these days it seems that anything more than 5' (1.5 M) deviation is cause for alarm, so the UK's "climb straight ahead" is needlessly confusing.
Most of us know how to "fly runway heading" and "fly runway track." What is the official CAA definition of "climb straight ahead"? If there is none, it should not be used, unless ATC doesn't care one way or the other...