What exactly is the difference between a regular conditioner and a product marketed as a "cowash" or "cleansing conditioner"?  Well, it's kinda complicated if you don't know what to look for.  
Regular conditioners are meant to condition the hair.  They are often cationic (positive charge) in nature and help to soften, detangle and smooth hair.
 

The difference between regular conditioners and  products dubbed as "Cowashes" is that usually a true store-bought Cowash has an additional ingredient which is meant to help clean without stripping the hair of its natural oils.

The additional ingredient is usually detergent-based or something like Liquid Castile soap or Liquid African Black soap, if the product is a more natural-based product.

For example, Shea Moisture Coconut & Hibiscus Co-Wash Conditioning Cleanser has African Black soap extract, which helps contribute to its cleaning ability.  

Camille Rose Caramel Cowash uses Sodium Cocoyl Taurate and Cocamidoproryl Betaine.  Both of those ingredients are sufactants used for cleaning.  

But there is no hard and fast rule for cowashes.  

To make it complicated, there is a process which many Naturals use which is called "cowash".  Simply put, it's the process of using a cheap, regular conditioner (TRESemme Naturals, VO5, Suave etc) to help displace and remove most of the dirt/oils from the hair/scalp.  With this process, you skip the use of traditional shampoo and simply use your conditioner to both help remove dirt/oils and condition the hair.

This is different from using a product labeled as "cowash" in your hair.  Most of the regular conditioners Naturals use to 'cowash' with are just that: regular conditioners.  They don't have any overtly labeled detergents or natural soaps in them.

If that wasn't complicated enough, technically, you can also turn a regular conditioner into a real conditioning cleanser by adding something like Liquid Castile soap, Liquid African Black soap (black soap melted in water), Decyl Glucoside or "Polyglucose/Lactylate Blend" to  it.  

By doing this, you have just added the detergent-based ingredient or natural soap-based ingredient to a regular conditioner, making your own DIY cowash/cleansing conditioner.

Either way, "cowash" is a term which seems to have originated from the natural hair community and appropriated by companies as a way to market a specific type of product to that community.  

Whatever you decide to use, give the most attention to what you want to do with it and the ingredients of the product itself… regardless of how it's labeled.

Related
http://shop.camillerosenaturals.com/caramel-cowash/
http://www.drugstore.com/sheamoisture-co-wash-conditioning-cleanser-coconut-and-hibiscus/qxp512930?catid=183477
http://www.ewg.org/skindeep/ingredient/704595/PEG-40_CASTOR_OIL/