You have spot color where you can count each individual color. A four color spot print might include something like black, white, red, blue. Spot colors may be 1 or more colors.
A process color print uses four transparent inks, magenta, cyan, yellow and black to produce many colors, like a photo. The inks go down wet on wet and depending on many variables, mesh, halftone, etc.; will combine to produce different colors. Black is not strictly necessary but its tough to get rich blacks without it. Look up Subtractive Color Theory.