Erm? I don't know where you're from, but in all countries I've been to burger refers to the bread style used to hold the contents together.
Salad is usually simply a mix of raw fresh vegetables.
In the United States, "burger" almost exclusively means a hamburger made of beef. Or a substitute meat, but it must be ground meat. Turkey burger, ostrich burger.
A "chicken burger" is usually called a "chicken sandwich". I agree that the "burger" nomenclature is better, because you know it's on some kind of roll. A "chicken sandwich" could be on anything.
As far as "salads" go, everywhere I went in New South Wales anyway, the plural "salads" referred to individual vegetables that can be used as toppings on sandwiches, etc. The singular "salad" was as you describe.