I think I can help you out. The difference between Ivory and Bark is basically texture, color, pattern. Ivory is going to be what most people think of when the think of typical ivory such as elephant tusk, walrus etc. The bark is the outter layer of a tusk for example, and the ivory is the inner core. Bark is going to have texture and pattern as its been exposed to atmosphere, use, etc. The ivory is going to have little variation in pattern, but will vary from white, yellow, caramel.
Here is a picture of an Ivory inlay...you will see it is almost white. In my opinion the whiter the better for ivory.
And here is an example of Bark
You can see the cracks in the bark, and different colors like greens, and blues. Again my opinion is the more cracks, and the more green and blues, the better.