I tend to teach the horse as I see it in front of me but yes different types generally need different exercises.
In your example of the hunter type jump v the fizzy pony I would not only find out what they wanted to do with their jumping (working hunters need to jump differently from show jumpers). I would do more flat work with the horse working on adjusting stride length particularly in canter but with the pony concentrate on improving the jumping work on track and rider control before and after jumps.
For every horse I teach I've roughly similiarly goals where I'd like them to end up (pleasure to handle and ride basically!) but I usually get there in different ways. Depends on the horse. You'd probably start off doing dirrent things in different ways with a started nappy bargey horse different to how you'd treat an unstarted nervous horse. Figure out your goals, then figure out how what your horse needs to here from where he is now, to that goal.