I think Sack-Religious has the right answer.
It's impossible to get a straight answer about an injury out of a Tom Coughlin coached team; he fines players for discussing their injuries with the media. Still, every indication seems to be that Burress has a lower ankle sprain of a moderate degree. I suppose it's possible that Burress could play this effectively with torn ankle ligaments, which is what the most severe degree would imply, but it's doubtful. It's more likely that he has a serious sprain with some tearing and maybe some pain from bone spurs, which he's had in the past with his other ankle. He's risking a more serious injury (complete tear or other compensatory injury) by continuing to play, but playing is mostly a pain tolerance issue if his ankle joint has been deemed stable enough to run and cut.
DJ Hackett has been reported to have a high ankle sprain, which is entirely different than a lower ankle sprain. The "classic" ankle sprain affects the group of ligaments that hold your outside lower leg bone to the bones at the back of your foot and help to stabilize the ankle joint itself. A high ankle sprain involves some tearing of the wide ligament fibers that make up a joint between the two lower leg bones. Again, return to play depends on stability, and, since it involves a joint critical to weight-bearing, is often associated with more pain and longer healing times.
Although both injuries are referred to as ankle sprains, they are totally different types of sprains because of the types of "joints" involved.
If you can visualize injuries better with images, here's the difference in pictures:
Ligaments involved in lower ankle sprain
Ligaments involved in high ankle sprain
BTW, I don't get into as many SP threads during the season with my IDP responsibilities, so feel free to PM a link to the injury threads (or questions) if you think these kinds of posts are helpful. ATC1 and others (trainers, MDs, PTs, etc) are usually well on top of things, but I'm happy to throw my thoughts in, too.