A polymer medium is a liquid that is transparent once dried. In some cases, the medium is used as a glaze to seal and protect projects. You can add a polymer medium to oil-based paints to extend the drying time of the paint; this enables you, as the artist, to make adjustments prior to the paint drying out. You can also use a polymer medium with watercolor crayons to bleed colors together; moreover, you can use a polymer medium as an adhesive to hold materials together. The liquid also increases a film's integrity by drying clear -- without sticking -- and does not change the look of the film.
You can add glaze to oil-based paints like acrylics to extend the life of the paint. The main purpose of glaze is to protect a piece of art from the elements. You would brush or roll the glaze onto a piece of work to seal it from the elements. Glazes dry clear but may also add additional shine and depth to artwork. Glazes also come in colors, while polymer mediums don't.
Glazes are used in design and specifically for faux finishes on walls. Glazes can highlight and bring shine to paint to highlight a painted on effect, such as faux marble. Glazes are also used to seal a particular look in place, for example, a wood rubbed through look, where the grain of the wood shows through the paint in defined areas, and those areas are then sealed with glaze to keep the paint from chipping away, exposing larger sections of wood.
Glaze has a much different meaning for ceramics. Glaze is a thin layer of glass that is added to a piece of pottery or artwork, then fired in a kiln. The glaze dries creating a shiny exterior to the piece while protecting the piece from exposure to moisture. Underglaze is also used, which adds colors to the piece of work. Overglaze is applied and the piece is fired. The overglaze provides the transparent glass layer to the piece.