Types of Soap
Hard and soft, and everything in-between. Often hardness is achieved through the addition of hardening agents, so many natural soaps tend to be softer. Hard soap can be produced by repeat regrinding and re-forming, known as triple milling.
Keeping the moisture content low helps the hardness of the soap, but this is often achieved by accelerated curing in very low humidity conditions.
Glycerine is a normally produced during the soap making process. Glycerine is a humectant, which means it attracts water. Therefore soaps with glycerine in them tend to make your skin feel moister. At the same time glycerine soaps tend to have more water in them and attract water from the atmosphere, therefore 'sweating' in humid conditions. Many commercial soaps have had the glycerine component removed during manufacture as it can be sold separately.
Uses slightly different components and usually some form of alcohol to alter the process. The process is also conducted at higher temperatures. All these facts change the process and hence the resulting product. NOT all transparent soaps are glycerine soaps.
Are actually quite difficult to make and many of the commercial liquid soaps are just in fact detergents: They will clean just fine...
"Dove®" Soaps (a registered brand) are more correctly labeled "Cleansing bar" as they are primarily made from synthetic surfactants, and do not have "soap" components in them. This enables a pH neutral claim, although soaps can be made to be pH neutral.