...It's like the iPad has an IPS panel, and the Air doesn't. ...
The iPad DOES have an IPS display, and the macbook air does not, you've got it exactly right.. but this isn't a hidden fact. Part of the marketing for the first iPad was about the "gorgeous" IPS display..
Why in the world would the iPad have a better screen than the Air? Is there something I'm missing?
It's pretty simple why the screen on the iPad would need to be of a higher quality -- touch. You're not holding your air, or any laptop, 8-12 inches from your face and touching it all day long, in multiple positions. A laptop is generally used in a set position, where you're adjusting the screen to fit that position.
This is no different than the macbook pros. They have a better viewing angle than the air, but you're also paying a premium on the entire computer over the air. The 13" air is a much better screen, in my opinion, than the 13" pro.
That being said, I own a 13" air, and an iPad 2. The iPad screen is beautiful, but i love my air as well, but in the end, they're serving different purposes, and that's why the screen is different.\
Edit:
I wanted to add, the iPad is made up of a screen, and a backside. You are only interacting with the screen, and so I certainly hope it's a high quality screen. The air you're interacting with multiple things. The touchpad, the keys, and looking, but not touching, the screen.