No, solid shampoo is not the same as soap.
Soap is created by mixing oils and lye together which creates a chemical reaction called saponification. Most people that make soap add extra oils to add moisture to your skin, this is what creates the soap scum that can be left in your sink. It is also the reason soap marketed as shampoo can leave a weird waxy build up on your hair. Bar soap has a high pH designed for skin not hair so when you use soap on
your hair it can cause build up, oil removal, dryness, breakage and damage. Using products designed specifically for hair is the best way to keep your hair healthy, lustrous and manageable.