A dual-stage overdrive or distortion simply means the circuit has 2 gain stages or SUB-circuits. It processes the signal into OD/Dist then passes it on to a secondary amplification stage to further modify the waveform. I find multiple gain stage pedals exhibit a "cleaner", smoother, & more distinct sound. Single gain stage pedals really break up chord articulation. The Boss MT-2 Metal Zone is a fine example. To me, it has a very good distortion that doesn't turn your chords into mud. Clarity comes to mind.
Cascading means that one process or stage passes on to another, then perhaps another. Think of a bucket-brigade delay with feedback or return up high.. it'll go into self oscillation as the signal passes through the stages & back around again. For a OD/Dist box, the two terms are near synonymous with each other. The signal "cascades" (like a waterfall) from the 1st gain stage into the 2nd.
thanks defrag. i read that the od-3 is dual stage while a jaques od (tubeblower II, i think) is supposed to have a cascading circuit. so cascading can be also done by having an od like the od-1 into another od like the tubescreamer or probably the ultimate: two od-3s together or two mt-2s dual staging and cascading into each other. perhaps i'll try that as soon as i have them.
edit to my previous post 02/16/2008 o2:49:52( i cant find the edit icon ) its not a jacques tubeblower but an overtube with a switcheable cascade circuit.