Glycerin Soap or Glycerin in Soap
Glycerin is a natural by-product of soap making that enhances the moisturizing properties of handmade soaps. Therefore, all handmade soap has natural glycerin.
Then why some soap is called "glycerin soap"? Because it uses (among others) vegetable glycerin as a solvent, which gives the transparency looks of glycerin soaps. At least, it's the explanation that makes sense to me... If you find another one more interesting, or more science-based, place a comment below!!