I feel there are two ends of the spectrum, with a great deal of grey in between.
At one end, you have a person who doesn't realized they've vanity published, just spent wads of cash to have a press design the book, and are sitting around waiting for their name to show up on the best seller list.
On the other, is the person who registers the business name, does all of the design/formatting/cover contracts, deals with the printer themselves, and does all the legwork to be shelved/placed/promoted.
As you can see, there's a LOT of room in between.
After some headache inducing research, I've found one definitive answer:
Who owns the ISBN?
If you bought it, and have all the control, you're technically self published. If the press owns it, vanity.
This has no bearing on my personal thoughts about vanity OR self publishing, it's just an easy and clear measuring stick.
So that guy/gal who has books printed to sell in the back of the lecture hall - could be either. As with any other method of distribution.
Doesn't say whether one way or another is better for you personally, either. That really isn't up to me (or anyone else) - just a matter of how many headaches you want to take on yourself.
Sort of. Man, this can be a confusing industry.