>>21604545
There's a sliding scale of correctness to either of these.
If the chicken is whole or sliced, it is not prepared in the style of a Hamburg Steak, so, even if it is served on a kaiser roll or similar bun with toppings usually reserved for a Hamburger Sandwich, it is more correct to call such a thing a chicken sandwich than a chicken burger.
If a chicken patty is served on toast, the usual term is a "Melt". Still more of a chicken burger than a sandwich, but changing the term helps mitigate unwanted surprise.
If I asked for a t-shirt, and you handed me a button up collared shirt with short sleeves, I would be similarly surprised in a less than exuberant way. They're similar, but the convention is that a T-shirt is stitched along the sides, closed in the front and back, and not V-necked or collared unless specified.