Fundamental Differences
The differences begin on the most fundamental level. A zircon is crystallized zirconium silicate. Diamonds are an allotrope of carbon.
Color and Rarity
Zircons are uncommon in rock shops and are usually brown, red, yellow, green, blue, black or colorless. Diamonds usually have a yellow or brown tinge, with actual colorless diamonds being quite rare.
Uses
Colorless zircon gems are occasionally used as false diamonds, but all manner of zircons can be made into attractive gems and jewelry, while diamonds are commonly used in heavy industry, such as oil drilling, as well as for jewelry.
Hardness
Zircons, while harder than most natural gemstones, pale in comparison to the hardness of a diamond, which has the distinction of being the hardest natural mineral known.
Misidentification
Colorless zircons are sometimes misidentified as diamonds due to visual similarities of the two stones.