Can a 110 v extension cord be used with 220 v current if the proper adapters are used at the plug ends? In other words, is there a gauge difference in the wire used in 220 v extension cords and 110 v extension cords? I realize that the wattage drawn does make a difference.

Can you? Yes. Should you, No. Don't use adapters, rewire with the correct plugs and outlets. There is no neutral in 240 so one of the conductors would have to be recoded as a conductor. There is no difference in the wire used. Most cordsets, at least those for extension uses, are rated for up to 300 Volts.