White wheat is actually a different wheat - and it provides a slightly malty flavor to the beer and has higher protein content. The color differences are small (< 0.5 SRM). Both are malted.
Belgian Wit is typically made from unmalted wheat (torrified or flaked wheats are easiest for the homebrewer to use) as opposed to white wheat malt or regular wheat malt.
White wheat can be used in Weisse, and is appropriate for Bavarian weisse due to its malty profile.