Red and white wines are made differently, so there are different factors to consider when deciding on what yeast to use. White wine is basically just fermented grape juice, while red wine is made by fermenting "must" which includes the skins, seeds, and stems of the grapes as well as the juice.
Typically red wine is fermented at a high temperature (85°F), while whites are fermented at lower temperatures (68°F). Thus red wines require a higher heat tolerance for their yeasts to avoid stalled fermentations.
Taste is also a big factor to consider. For example, white wines typically have more fruity esters, and the choice of yeast determines the level and variety of esters you will get in the final product.
Either yeast will work for fermenting both types of wine, although you do have to consider the yeast's optimal temperature range carefully and not go too far outside of it. A yeast that is classified as red or white generally will impart flavors typical of that style, but I would view it more as a recommendation than a requirement.