What ingredient(s) makes it a "cleansing" conditioner appropriate for "co-wash" then? Are Cetyl Alcohol and Cetearyl Alcohols cleansers?

Is a DevaCurl No-Poo a "co-wash"? I ordered a product from Ouidad called Ouidad Co-Wash (contains Behentrimonium Chloride), which I thought was a "no-poo", but now I think I have no idea what I'm using...

Are the products that call themselves "cleansing conditioners" (Hair One, Wen, Daily Fix, etc.) "co-washes" but not"no-poos"?

I think I've had these definitions wrong all along...maybe...
3b/c, Coarse, Low Porosity, Desert Climate
CG since August 2011/Occasionally Minimally Modified since 2013
Favorites: Beautiful Nutrition Cocoa Curl Cleansing Conditioner, Beautiful Nutrition Cocoa Curl High Definition Moisture Gel, Beautiful Nutrition UltraLight Lime Jel Control Serum, Beautiful Nutrition Lemon Rinse Clarifying Treatment