Another way of looking at it is that if you're going for a Big Money-like strategy, you're expecting and/or hoping to never draw two actions at once; a single turn might be one play of smithy, or maybe one play of mountebank, and if two collide that's bad. In Laboratory-BM, it's okay for labs to collide, but if you're buying labs with 4-5 and golds with 6, the collisions aren't necessary for you to do well and you're okay if they never happen.
Whereas in the Hunting Party deck, you're expecting/hoping for a typical turn to involve drawing and playing multiple hunting parties.
That's the difference that I've always thought. BM+X is a strategy where you expect to play zero to one X per turn (besides treasures), whereas an engine would be where you expect to play multiple actions every turn.
The rest sort of flows from that.