Unless you buy a really cheap shampoo that says Wash and Wax, the "WAX" part is not a lie. Dont expect that after you wash your car you will end up with a wax coating on the paint that will make the paint look great and protect it for a weeks or so. This does not apply even to the most highly regarded detailing brands that offer Carnauba boosting Shampoo's.
What the "WAX" really stands for is a booster to the existing wax. Suppose you have a layer of wax on your car. The wax brand states the wax will last for 1 month in harsh conditions ( Pakistan environment ) and you have to wash the car 3 times during this time. There are two types of shampoo you could use. A simple Wash shampoo (No boosters) or a combined Wash and Wax (Carnauba) shampoo.
The basic shampoo will help you maintain the 1 month durability by not hindering the performance of the wax while cleaning the car. On the other hand, the Wash and Wax will also boost the durability of the wax with every wash ( could be for a few days or even a week ). So in the end, you might see the wax last more than the 1 month period by a considerable amount.
Shampoos do contain wax even if its in very low quantities. But this is more than enough to boost up your existing wax to help increase the durability even if its by a small amount with every wash. In the long run this adds up.
I tested my AG shampoo on a car that was never polished/waxed in its life. After the wash, there were beads on the paint. These beads were no where near the perfect round beads you would get with a dedicated wax but the beading was there even with a simple wash using a carnauba boosting shampoo. Beading that lasted 4 days for a car that stood in the sunlight all day and was used like a donkey. Yes it was a mehran. My testing dummy car I like playing with.