"Tallerken" is what you eat your food from. It's a dinner plate. "Plade" means 'plate' in other senses, like a metal plate or a tectonic plate. For example, a number plate (for a motor vehicle) is a "nummerplade". It can also refer to a music disc like a vinyl LP or a CD. Examples: "Man plejer at spiser mad fra en tallerken." (One usually eats food from a plate). "De tektoniske plader bevæger sig i forskellige retninger." (The tectonic plates move in different directions.) "Hun satte en plade på grammofonen" (She put a disc on the gramophone).

If you say "plader" then it will sound really akward. Use tallerken (singularis) or tallerkner (pluralis)