Also, soap and shampoo bars are the way to go instead of liquid versions - less plastic waste.
If you're concerned with dry/sensitive skin, try to find ones without SLS (Sodium lauryl sulphate), it's a foaming agent used in loads of soap products, but it's actually an irritant.
It is a detergent, but I don't think that means you can call it a soap. I could be wrong though. The best soap has the glycerin left in, so it's moisturising your skin even as the detergents are drying it out.