A hammer drill is not used for driving a screw.
Don't tell that to my hammer drill, it would forget it has the ability to drive. This is why companies put speed selectors and mode switches on hammer drills. I've used a hammer drill for driving plenty of times, all you do is switch it from hammer mode to driving mode.
Now, if you're talking about an SDS, that's a different animal altogether.
The difference in impact bits versus standard bits, in any type of drill/driver, is its ability to handle impact. They're made from different materials that are designed to take the force that an impact driver puts out. In most situations you won't notice the difference in regular drill/drivers, but putting a standard bit into an impact, you run a stronger risk of breaking the bit.