I was eavesdropping by the ingate when a big grand prix jumper was schooling her kid in the jumper ring (i wanted to listen to as much as I could from her!) and she said "get your work done in your corners and the jump will be there". You trainer is absolutely right when she says corners are important. It doesn't matter if you ride jumpers or hunters, get your work done in your corners! That's where you set your horse up for the jump. Find your line to the jump, where you get on your pace, etc, approach is EVERYTHING. The difference is that your approach will be different from the hunter ring. You don't go to the end of the ring for your corner, you make your corner. But they are still extremely important!
It's not a completely different world from the eq world actually (which is why lots of big eq riders also do the jumpers and transfer so easily to the GP ring). Believe it or not, but jumpers is NOT about running around as fast as you can. Jumpers who just gallop around making everyone gasp drive me nuts. Sure, you might be successful at first, but once the fences are raised it'll bite you in the butt if you can't do more then that. Some of the best and fastest times have been from careful riders who could turn on a dime and jump on an angle.
So what's the difference? You're going to want your horse more on his haunch then long and low. Forget having a 12 foot stride everywhere, you put your horse on the stride that's needed in that part of the course. Which means your horse is going to have to be very adjustable and responsive. Flatwork is your best friend! You CANNOT be successful in the jumper ring without good flatwork.
Also, there's more then one kind of jumper class (they're called "tables"). It's not as simple as "whoever does it fastest w/o knocking rails" wins. Sometimes there's a jump off, sometimes not, etc. know your tables to know how to win the class! Let me know if that confuses you and I'll describe some tables!