Technically, any animation that involves a silhouette moving on a contrasting background could be considered silhouette animation, but the original silhouette animation technique was almost more a form of puppetry using what was essentially hinged paper dolls with their parts tied together with wire. These dolls were positioned against a solid backdrop on an animation stage and filmed with a rostrum camera, and repositioned accordingly with each frame, moving in sequence and posed much like hinged and jointed dolls. In some ways silhouette animation in this style was a type of cutout animation, using the same frame-by-framing filming techniques with a cutout silhouette of an animated character or object.
Cutout animation can also be used in its more traditional method to create silhouette animations. Black cutouts can be moved against a white backdrop to simulate an animated silhouette effect. The only difference, really, is that the cutout pieces aren't tied together with string. This effect can be very simple to accomplish when the animation is just an unchanging object moving across the background area, or it can be extremely complex if the silhouette has to change size, shape, or angle, often requiring multiple silhouettes tracking motion across a frame.
Another form of silhouette animation can be accomplished using a particular technique of drawn-on-film animation, in which film frames are exposed to light with objects placed on them. The exposure creates an imprint of the object on each frame, burning a silhouette in. As the objects are placed differently in each subsequent frame, they create a drawn-on-film animation rendered directly on the film reel.
Traditional animation can also be used to create a silhouette animation effect, even if technically it's just black-and-white drawings - black cel paintings on a white backdrop, white cel paintings on a black backdrop, etc. It still follows the animation principles of keyframing and in-betweening, rather than the more sequential methods of true silhouette animation. The same can be said for silhouette animation made using digital animation methods, whether 2D animation in programs like Flash or 3D animation in programs like Maya. While the look and feel may be the same, the methods are wholly different - but no less striking in their overall effect.
Whether using classical silhouette animation, digital, traditional 2D, cutout, or drawn-on-film animation, it's possible to incorporate color as well - though it's generally a single-color silhouette against a black or white backdrop, a black or white silhouette against a single-color backdrop, or a single-color silhouette against a single-color backdrop. Incorporation of any additional colors, unless done in very specific ways, would render it no longer a silhouette animation.