The difference starts with sigma bonds. Electrons are disabled by nuclear attraction from both bonding nuclei, while within pi bonds, electrons are loosely held in the general proximity of either bonding nucleus. All pi bonds are naturally delocalisable. People are most commonly used to call it “double bond character,” but since it can occur for triple bonds as well as bonding that never even fully constitutes a double bond, stigma character and pi character are more appropriate, in my opinion.