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Just doing a quick google search, the only difference I see is that the aquarium lights come with two cords and on/off switchs and the plant grow ones only come with one.
If you mean the bulbs, then the difference would be color. I think grow lights are low on the Kelvin temp scale...like maybe 4-5k or so. For an aquarium you want a higher K temp. A daylight bulb is 65K.