You didn't give details as to which cart models these refer to; or the size of the fire box on the carts. So this leaves a little bit of guessing.
The cart with 3 burners: The 3, 1/3rd pans were to be heated directly. Check the depth of the fire box, I think you will find it is not deep enough to use a 'spillage' pan as a 'bain marie'. Depending on what is being heated, once the water is hot the burner is set is a low to maintain the water temp. ... Next I think on most days when the two outside pans are hot, their burners may be turned off as the heat and hot air from the middle burn might be able to to keep those pans warm ( depends on the outside air temp). Of course, these could be used as deep fryers if needed.
Carts with 2 burners: There are two situations here.
First, a cart with top of fire box sized for 1 full size 'hotel pan' or 3 1/3rds (20" x 12"); and with 1 or 2 burners. This should have a spillage pan to be used as a 'bain marie' to heat the insert pans (three 1/3rd pans). One burner can do the job, but two burners can heat the water faster. Then the 2nd burner can usually be turned off.
Next, a cart that has a full size 'hotel pan' ( 3, 1/3rd pans) and a 4th 1/3rd pan. The fire box top is appox 26" x 12". A full size spillage pan is heat as a 'bain marie' with one or two burners as described above to maintain food at minimum serving temps. The 4th 1/3 pan has it own burner for higher cooking temp and could be used as a 'deep fryer'.
Hot Dog carts are built to used outside and sometimes in cold weather. Burners are cheap for the manufacture/builder, about $25 to $30 each (8,000 btu or 13000 btu) and adds a convenience for the Vendor. More burners is for faster heat up, but once hot, the burners are set to low. Water boils at 212 deg F, above this is steam. The Vendor doesn't want to boil away all the water, only maintain a temp (140 to 200 deg ???).
The counter top Warmer. This is intended to be used on the counter inside, and not outside in cold weather. It clearly states to be used with a 'bain marie' pan. Thus it only warms/heats water to 200/212 deg. Since this is a gas appliance without a thermostat control, water is the heat regulator to keep from burning food at the bottom of the pans. If used as a 'cooker' per the advertisement, it is a slow cooker at 200 -212 deg F. ... A low BTU burner is used to keep the Vendor/user from setting the counter or table tops on fire, and/or needing ventilation hoods to be installed.
<message edited by edwmax on Fri, 08/30/13 5:47 AM>