If I recall, a Dye which needs a LONG strategy is relatively insenstive to the reduced laser exposure at the start and end of a mark (T3 pit) - so a LONG exposure, covering the required mark with beam centre to centre is needed.
SHORT strategy, implies the dye IS sensitive to edge exposure from the laser spot as it travels, so a short exposure covering the required mark including the trailing edge of the ON and the leading edge of the OFF is called for.
No direct correlation with what you use them for, other than that Cyanine tends to degrade faster with UV.