Are soaps made of wax?

Soap is actually the product of a chemical reaction between an oil, grease, fat or wax and a strong alkali - 'lye' or sodium hydroxide. The oil or fat contains fatty acids and the reaction between these and the alkali produces a salt which we call 'soap'. This salt has the property that oil and grease will bind to one end of the molecule and water to the other, so making grease and dirt soluble in water. Depending on the oils or fats used, different products result and some may contain more free waxes and other substances than others, so you are partly right but also wrong in that the soap holds together by itself: it doesn't need any wax to bind it.

yes there are made of wax but they are expensive just like the candles made or real wax.