the direction of a great circle joining those points will be different except at the point half way between them.
I think that was what StudentATP was asking. If I steered the equivalent direction of the average great circle track between two points, (from the starting point) then I would make my destination by a slightly longer route as Andi pointed out.
e.g. steering due West (true) across the Atlantic from London, would get me to Newfoundland and I'd never get to the N. pole. (i.e. along a line of Latitude)