Acne is the overall skin condition that causes outbreaks of lesions and pustules.
A pimple is an individual pustule, or raised bump, on the skin as a result of acne. If you saw someone with a lot of pimples on his face, you might say to yourself, "He suffers from acne."
"Spot" is British slang for a pimple. Pimples are also called "zits" in American English, but never "spots."