If you use the Express Service then they are replacing the whole device and so you’re charged the full replacement fee. You’re getting a new battery, new screen, new back glass, new housing, everything. If you go into the store they will replace just the screen for the lower price. It even states this in the link you provided.

How much will it cost?

If you have AppleCare+, you can replace your iPhone with an incident of accidental damage. You’ll pay the “other damage” AppleCare+ fee, as specified in the AppleCare+ Terms and Conditions.