A single stage regulator has one regulating mechanism which reduces the cylinder pressure from around 55-60 bar to 1-2 bar in one stage. The needle valve then fine tunes the output flow. A dual stage regulator is easily recognisable because it's much larger and often appears to be two regulators in one - which is exactly what it is. A dual stage has two regulating mechanisms which reduce the cylinder pressure in two stages. The first stage is preset and reduces the cylinder pressure from 55-60 bar down to somewhere around 5-10 bar. The second stage then reduces from 5-10 bar to the required 1-2 bar working pressure. Again, the needle valve then fine tunes the output flow. A needle valve doesn't affect the output pressure.
If you search google for single and dual stage regulators, the difference in appearance will jump out at you. None of the aquarium regulators sold by Dennerle, JBL, Lunapet, TMC, D-D, or anyone else I know of, are dual stage. If it isn't marked as dual-stage, multi-stage, two-stage, or some variation of that, you can be fairly positive it isn't; but I've seen some aquarium regulators marked as dual stage when they're simply dual gauge, so you have to be careful about that.
In a single stage, any fluctuation of the cylinder pressure results in a slight change to the output pressure, with resulting erratic flow from the needle valve. In a dual stage, fluctuations in cylinder pressure shouldn't affect the output pressure until the cylinder pressure falls below the preset 5-10 bar, by which point the cylinder is almost empty anyway. Dual stage regs can seem like overkill, but they're invaluable if you want a reg that you can set and forget. Provided you change the cylinder before it's completely empty, you should rarely have to touch the reg or needle valve at all once you get the settings how you want them. That's why they're used in hospitals where a change in gas flow could be fatal... just as they can be for our fish and plants.
If you want a fairly cheap UK-made dual stage, CS Milne sell them for £55. Personally I'd look on eBay, though. I recently bought a used Harris dual-stage from America for £80 including shipping. Surplus lab stock in near perfect condition. It would have cost something like £500 to buy a brand new one.