A beard wash and beard softener is a product that's designed specifically for your beard. A traditional hair shampoo and conditioner is designed for your scalp and hair which contains more sebaceous glands and thicker skin than anywhere else on the body.
A premium beard wash will have a gentle lather that matches the fragrance of your favorite beard products like beard oil and mustache wax. A beard softener is like a conditioner in that you use it after washing and rinse while in the shower. A softener will help make your beard softer, shinier, and easier to comb and manage.
Silicones can be harmful to your beard over a long time of usage. Many silicones aren't water soluble and will build up over time. This will leave your beard looking dull and brittle. It also requires you to use harsh shampoos to remove the silicones. So you start this vicious cycle of over washing and over conditioning.