Soaps are sodium or potassium salts of long chain carboxylic acid whereas detergents are ammonium or sulphonate salt.
Cleansing action of soap : The ionic part of soap molecule dissolves in water and the non-ionic part dissolves in oil. Thus soap molecules arrange themselves in the form of micelles, pulling the dirt or grease from the cloth. On rinsing with water, soap is washed off, lifting the only dirt particles with it.