Mileage programs give you points when you fly on a particular airline -- this is part of their customer loyalty program. Joint mileage programs are where two or more airlines cooperate to offer their passengers points. This gives passengers more flexibility in choosing airlines and helps them accumulate points faster than if they were receiving points from individual airlines.
Example: Mileage Program
RedAir offers RedPoints
BlueAir offers BluePoints
GreenAir offers GreenPoints You have to redeem your individual color points from each airline's points catalog.
Example: Joint Mileage Programs
RedAir, BlueAir and GreenAir all offer RewardsPoints. You can redeem your combined RewardsPoints from a common catalog shared by all three airlines.
On a grammar note, I'm not sure you "redeem from," but you get my meaning.