In this paper, we propose a generalized method by designing new response systems for solving synchronization problems of coupled chaotic identical and non-identical dynamical systems. We extend our study by considering two new techniques for constructing a chaotic synchronization between two identical or non-identical dynamical systems. The first one is based on the classical Lyapunov stability theory. The proposed method is analyzed by means of equilibrium points, eigenvalue structures, and Lyapunov functions. The second one requires the nonlinear part of the response system to be smooth enough and uses the expansion of such a function. The designed controller functions enable the state variables of the drive system to globally synchronize with the state variables of the response system in both methods. The global convergence of the proposed methods have been discussed by giving two theoretical results. To show the effectiveness and feasibility of those approaches, various numerical simulations have been carried out.