What is the difference between a single and double treadle spinning wheel

Both with a single and double treadle base you can treadle with one foot. This gives you the opportunity to sit at an angle to your spinning wheel, not straight on.

If you use two treadles, your treadling will be lighter, but you will sit directly opposite your spinning wheel. You benefit from the double treadle base when spinning with higher ratios, which requires more power.
The S10 Concept can be easily changed from double to single treadle. Each treadle base is a separate accessory. The S10C can be equipped with different style wheel and your choice of drive system - scotch or irish tension

The Victoria is a folding wheel and is equipped with double treadles.

The S17 is an unfinished wheel kit that is comes standard with a single treadle.