The differences usually reside in actuation force (how much force is needed for the switch to register), noise level, and whether or not there is tactile feedback (a bump when you hit the key).
Cherry MX Reds are considered the "gaming switch" because they have the lowest actuation force, are basically silent, and have no tactile feedback. This is great for fast paced games that require very quick feedback.
Cherry MX Blues are considered the "typing switch" because they have high actuation force, are quite loud, and have sharp tactile feedback. They are very clicky and because of its actuation force it prevents mistyping if you accidentally fat finger a different key. The tactile feedback makes sure you hit the key that you want to...