What does the "bagel" setting on toasters do?
Unfortunately, the function depends on the manufacturer.  

While turning off a set of elements may be common, another option is that the setting may just increase the cook time.  Bagels are thicker and have more mass than sliced bread, so a longer toast time is necessary to have a similar level of toasting.

In particular there are Cuisinart toasters where the bagel button only lengthens the time of the toasting and does not change the pattern.

From Cuisinart PDF manual


  Bagel button 
  
  The bagel feature adds extra time to the toasting cycle
  to allow for thicker breads. You may also use the bagel button for
  English muffins and other thick breads.