Recoil determines the amount of kick your crosshairs move by with each shot. Thus, if you have more vertical than horizontal recoil, this means when you fire one shot your crosshair will gain more vertical distance than horizontal.
Recoil recovery rate is how fast the gun settles to perfect accuracy after you fire a shot. If you tap fire shots, and manually wait for the recoil to settle off, you'll retain near-perfect accuracy. If you hold down fire, generally the recoil distance will outpace the recoil recovery rate, causing your aim to kick upwards.
Think of your aim as a diamond centered around your crosshair. Each weapon has a different sized diamond based on the recoil and type of weapon -- smgs and assault rifles with higher rates of fire will have a larger initial diamond. When you fire a weapon, your shot will always be fired at somewhere in this diamond. However, each shot you take will expand the diamond further, both horizontally and vertically, based on the recoil of the weapon. The time it takes for the diamond to reset back into its starting shape is the the recoil recovery rate.