Process color uses translucent CMYK inks laid on top of one another to fool your eye into seeing other colors (Similar to your ink-jet printer at home).
A spot color ink is a specially-mixed hue that is not made by combining two or more inks, but rather is a single ink of a specific color (like buying paint for your walls at the hardware store). Spot colors can be brighter or more saturated than process colors, or have special properties, such as metallic gold or fluorescent green.
We use process colors in printing packaging, and at times can use spot colors when printing on-disc. Spot colors are available in package printing for an additional fee.