The term minor planet means a solar system body other than the "normal" (8) planets, and other than comets and moons. The term includes dwarf planets, asteroids, and centaurs, and many near-Earth objects and Kuiper Belt objects.
The exclusion of comets presents difficulties: a discovered object may not yet be showing the characteristics, and when the characteristics finally show, they can show in degrees. Thus a body classified as a minor planet may later be considered a comet, or perhaps just somewhat comet-like.
The term SSSB (for small solar system body) covers both comets and those minor planets smaller than dwarf planets.
Referring to a minor planet or SSSB as a numbered object says it is an object with a provisional designation (which are based on given periods of time, numbering the objects discovered within each period), implying there has been sufficient observation that it could be identified in future observations.