Make sure to differentiate the double stroke roll and the double bounce roll. The double stroke roll is wrist, at least at relatively slower speeds, where you have two individual strokes (two singles per hand), which you would use for paradiddles (usually with an accent on the first stroke. Single stroke, single stroke, double stroke), and the double bounce roll is where the second stroke is the result of a bounce. So you strike the drum once and let it bounce once, alternating hands. The method with the bounce will allow you to play at much faster speeds than using the non-bounce method.
A lot of people just associate double strokes with bounces only, but there are two ways of playing it.