In topology, a finite region with no boundary is called a cycle . Circles and spherical surfaces are cycles. In general, if something is a boundary, it has no boundary itself. So boundaries are cycles. But not all cycles are boundaries.
Topology uses observation to distinguish various spaces.
For instance, on a spherical surface, every circle is the boundary of a region on that surface. Thus, spherical surfaces are topologically different from toroidal surfaces. The definition of figure needs to be fleshed out. In order to be a figure, a region must be bounded, that is, held in by a boundary. For instance, an infinite plane is unbounded, so it is not intended to be a figure.