These are two whites with very different characteristics, both of which are useful for the artist, depending on their current needs.
Titanium White is the more common of the whites used for painting. It"s known for being bright white, almost bluish, and has excellent opacity and high tinting strength. When mixed with another color, it rapidly lightens the color. The drawback of Titanium White is it can be over-bearing at times, especially when you are just looking to lighten the value a bit and not greatly change the color it"s mixed with.
Enter Zinc White. Zinc White is very transparent, and has 1/10th the tinting strength of Titanium White. The pigment itself is highly translucent, and compliments other transparent pigments, such as Quinacridones, Phthalos, and Hansas very well. You have more control when you add Zinc White. When you add it to another color to lighten it, it doesn"t immediately change it to a pastel shade, like Titanium White can. Both are great colors to have on hand, and you should test both with a variety of other colors to see their strengths and weaknesses first hand.