A glaze is a vitreous substance fused on to the surface of pottery to form a hard, impervious coating. This coating is typically applied after an initial bisque firing, although certain glazes can be single-fired. The application of the glaze is typically done by dipping, brushing, or spraying. Once the piece has been glazed it is fired again to a temperature appropriate for both the clay body and glaze used. Generally, these ranges will be either low-fire (pyrometric cone 05-06 is the general range for low-fire) or mid-range (cone 6 being the most popular range).
An under glaze is a decorative coating that you dip or paint on to green ware or bisque pottery. After an initial firing, you can cover the under glaze with a transparent or translucent glaze for added effect. While glazes tend to be vitreous and run together when fired, under glazes can be far better controlled and create a painted.