It is shown that tracking and stability concepts and properties are in general mutually independent. The goal of control by its definition is to ensure required output tracking of a controlled plant. It is explained why a stability property need not he either necessary or sufficient for output tracking, and vice versa, in general. Control should ensure demanded qualitative system performances in two different spaces, the dimensions of which are generally also different. This implies duality of the control task. It is shown in the paper how the stability problem can be embedded into the output-tracking problem. By solving the tracking control synthesis problem, we solve simultaneously the stabilizing control synthesis problem. A Lyapunov-like output tracking concept is explained. It is shown under which conditions it reduces to the Lyapunov stability concept or to the Lyapunov-like state-tracking concept. The paper presents recently introduced new control issues: (natural) trackability and natural tracking control of nonlinear plants. It exposes the necessary and sufficient conditions for natural output trackability and for natural tracking control ensuring both output tracking and stability.