Professional-grade paints have a higher pigment concentration and less filler, and generally use a wider variety of pigments, resulting in a larger color range. Usually made with a single pigment, they mix more cleanly and have better tinting strength than lower-grade paints.
Student-grade paints have working characteristics similar to professional paints but with lower concentrations of pigment and a smaller range of colors. More expensive pigments are generally replicated by hues, which may not have the same mixing characteristics as pure colors. They don't cover as well as artist-grade paints, but they're usually more affordable.