No, these terms represent distinct concepts.
“Clean label” focuses on the transparency and simplicity of the ingredient list (e.g. fewer additives), whereas "organic" refers to a legally regulated agricultural production and processing method, with strict regulations on synthetic pesticides and GMOs.
"Natural" broadly refers to the origin of ingredients but lacks a strict legal definition. A product can be "clean label" (simple ingredients) without being organic, or "organic" without necessarily having a "clean" or short ingredient list.