AC vs DC and ELF - extremely low frequency
The quote is incorrect on this bit: -


  In any battery-powered appliance the current flows from the battery to
  the appliance and then back to the battery. It will create a static
  magnetic field.


The above is wrong - most battery powered pieces of equipment consume a static current (basically the average current taken) and an alternating current superimposed on the static current. The alternating current produces alternating magnetic fields which can be detected.

An exception to this is a battery connected to a passive component like a resistor. In this case the current might decrease very slowly over time (due to battery exhausting itself) but the slowness of the current change (in the order of milli amps per hour) will not generate a field that is easily detectable other than by using a gauss/flux meter (they are also used to measure the earth's largely static magnetic field.