Ah, but the word bar refers to the shape. A cream egg and a cream egg bar have the same ingredients but one is bar shaped and hence called a bar. You can’t call something that’s not bar-shaped a bar.
There are, furthermore, two distinct types of rice crispie related sugary snack. The first is the type with just chocolate which is almost always made in a blobby shape in bun cases and is hence known as a rice crispie bun. The other type is the gooey version with toffee or marshmallow fluff or butter and stuff in it. These ones are made in a baking tray then cut up into bars or squares to serve. Clearly these aren’t buns and would be called bars or squares depending on the shape.
Neither qualifies as a cake though.