The typical tiger's eye is a shimmering golden yellow to brown stone. When it occurs as a blue-gray stone it is usually not called tiger's eye however. It is Hawkeye. Tiger-eye and it's related Hawkeye are made mostly of quartz with silicon dioxide inclusions.
It acquired its name from the illusion it creates of being eyelike when cut properly. For this reason, it is also credited, through sympathetic magic, with being good for the eyes, both physically and psychically. It is also useful in warding off the "evil eye", ie negative energies. As a balance of light and dark, it is also a balancing agent for the psyche and a symbol of all balances (night/day, summer/winter, life/death, yin/yang). Roman warriors carried it into battle for quick thinking and decisiveness in battle.
My books do not attribute any differences between gold and blue, Tiger-eye and Hawkeye, but the color and the names might indicate any differences to be found in applications. Blue more closely aligns itself with air, and the tiger-eye is typically aligned with the element of earth.