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 Modified since 2013
Favorites: Wen Cleansing Conditioner/Coconut Lime Verbena and Spring Orange Blossom, Pure Argan Oil, Pure Coconut Oil,
KCKT, KC Come Clean, Desert Essence Soft Curls Coconut Hair Cream, Eco Natural Curling Cocktail, Desert Essence Hair Defrizzer and Heat Protector