The easiest way to distinguish mold from mildew is their appearance: Mildew grows with a flat appearance and outward in a pattern along small crevices (like between bathroom tiles), often with a shape resembling a large dark spill. It's often greenish-black or slimy in appearance. Mold often grows in a pattern with many small circles and has a slightly fuzzy appearance, rising above the surface it grows on.
Both are found in different colors and shades, especially as they continue growing as the color may change as time goes by.
They're both microscopic fungi and many variations exist. Both grow when the right combination of temperature & moisture/wet surfaces exist. Both grow where organic material can supply them.
Mildew typically does far less damage and is easier to get rid of than mold. Often a good cleaner and a bit of scrubbing are all you need. However, mold causes permanent damage to the materials it grows on and often requires replacement. You may need professional service to safely handle mold damage.
Both can produce spores you may inhale, and some molds produce mycotoxins (toxins they release). This can lead to serious health problems, especially respiratory.