This paper is concerned with the Gaussian approximation (GA) smoothing estimation for the nonlinear system with the colored measurement noise modeled as an autoregressive process. Firstly, based on measurement differencing scheme, designing the GA smoothers with the colored measurement noise is transformed into deriving the GA ones with delayed state. Secondly, the novel fixed-interval, fixed-point and fixed-lag GA smoothers are proposed via the recursive operation of analytical computation and nonlinear integrals, as the general and unifying frameworks: they are applicable for both linear and nonlinear systems; by setting the noise correlation parameter as zero, they can automatically reduce to the standard GA smoothers with uncorrelated white noises; many implementations of the GA frameworks can be developed through utilizing different numerical technologies for computing such nonlinear integrals, e.g., the cubature rule based cubature Kalman smoothers (CKSs) with the colored measurement noise. Finally, the superior performance in estimation accuracy and computation efficiency of the proposed smoothing methods is demonstrated with a multi-sensor target tracking example.