Defining a "burger"

It depends on which side of the Atlantic you live on, according to separated by a common language:

The British focus on the bread: a burger is a cooked thing served in a round bun... So, order a chicken burger at Nando's or Gourmet Burger Kitchen, and you'll get what Americans would call a chicken breast sandwich. For Americans, a burger is a (chiefly AmE) patty made of (AmE) ground/(BrE) minced meat, so we can be heard to express surprise when the chicken burgers we order in the UK are chicken breasts. (Not necessarily disappointed, but surprised. One doesn't hear chicken burger that much in the US, but turkey burger is fairly common--and always ground/minced.)...

In fact the 'burger' is so much associated with the meat that (orig. AmE) hamburger can also be used in AmE to refer to ground/minced beef even before it's cooked. Hence Hamburger Helper, and its 'Add hamburger' in the top right corner of the package.

An American Burger

One example of many sandwiches that the British call 'Burgers'