Here is where different exercises get different names depending on the coach and what they like to see. The way I've heard snatch balances/drop snatches used is if there is any push at all, it's a heaving snatch balance. Strict snatch balance is just drop under that sucker and pop your arms up. Pressing snatch balance is going down slowly while pressing the bar up.
So using these terms, this is my understanding of the exercise you should use depending on your needs:
If you just need speed under the bar, do the strict, no push snatch balance. It's tougher. I think mainly for psychological reasons, because sometimes I'm ready to go and my brain says "What, you want to drop down with this weight on your back? I don't think so! We're staying right here!" Then it becomes incredibly difficult to force myself to drop.
If you need to get more comfortable with having more weight over your head, use a heaving-type snatch balance, as you'll be able to put up more weight with it.
If you need more overhead strength, do the pressing snatch balance.