An Eternity Band has stones - such as diamonds - all around the band. Hence the name "Eternity" as there is no beginning or end. An Anniversary Band, on the other hand, has stones only on the top/upper part of the band. The bottom part of an Anniversary Band makes part of the mounting that does not have any stones.
For a particular design, an Eternity Band is usually more expensive than an Anniversary Band because it holds a larger number of precious stones. Both types of bands could be given at any time - not just anniversaries - to celebrate cherished moments in your life.