Joint dislocation (also known as luxation) occurs when the joint surfaces become completely disengaged. A dislocation always damages the ligaments.
Joint subluxation is an incomplete/partial dislocation of a joint.
Joint Reduction is the process by which a structure is brought back into its normal anatomic position. (This term also applies to the bones in the case of fracture.)
Reduction can be spontaneous---ie, the joint simply "pops back into place". This process of spontaneous reduction, as you might imagine, is more common in joints that are not particularly stable, such as the patello-femoral joint. (Makes sense: easy out; easy in.)
Consider these drawings of the lateral view of the ankle, showing, left to right, normal alignment; a tibio-talar subluxation and then a tibio-talar dislocation:
And now think about the structural damage: with a dislocation, there could be a bone contusion where there is abnormal contact (shown below as the green "kissing contusion"); and the ligaments can either rip (as shown) or get really stretched.
(A subluxation can cause a bone contusion or stretching of the ligaments; a full tear is less likely.)