What is the difference between dual gauge and single gauge in voltage regulator IC?
"Gauge" is to do with the thickness of the heatsink provided for the IC

So great. Since we know that the temperature generated in an IC is the limiting quanitity on the functioning of an IC, your IC is as good as the effectiveness of your heat sink. What does a heat sink do? It removes heat from the IC and passes it onto the surroundings. Since your heat sink is a metal, it transfers heat through 'conduction'. Assuming 1-D conduction, i.e., conduction in only one direction, the governing equation would be -

Q = kAΔT/l


where--> Q = Rate of heat transfer(here rate of heat removal)

A = Surface area of heat transfer(here heat sink surface area)

ΔT = Difference in temperature across conducting wall(here temperature diff. between IC and surroundings)

l = Thickness of wall(here the thickness of your heat sink)

As you can see, the rate of heat removal is inversely proportional to the thickness of the heat sink. Hence, a single gauge IC, with a lower heat sink thickness will lead to a more effective removal of heat and hence better performance.