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.)
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