Acupuncture uses needles that puncture the skin. Acupressure does not puncture the skin, and uses pressure, usually through fingers.
You need to have a license to practice acupuncture, where acupressure some people just learn through books. I'm not sure if they need a license to practice acupressure or not in the states.
Acupuncture requires great accuracy, yet may be quicker to relieve the problem. Sometimes toxins in the body may be released also creating some side effects. Acupressure has fewer possible side effects and is more similar to a deep tissue massage.