How is hydrogen in heavy water different from hydrogen in normal water?

One or both atoms are a different isotope of Hydrogen, namely Deuterium ($\text{^2"H}$ a.k.a. $\text{D}$) instead of Protium ($\text{^1"H}$).
Deuterium ($\text{^2"H}$ or $\text{D}$) has similar but not identical chemical properties to the much more common Protium ($\text{^1"H}$) isotope.