Likelihood-approximation methods and contrastive learning (CL) are two prominent approaches for inference in models with unknown partition function. In this work, we provide a detailed comparison between the likelihood approximation by Geyer's approach (GA) and CL. Rather than increasing the complexity of Geyer's method to enable comparison, as proposed in [1], we adopt the opposite strategy by simplifying CL. We introduce a class of IS-within-CL schemes that estimate the partition function via importance sampling (IS) and reduce the optimization problem to the original parameter space. This perspective motivates the development of novel variants, whose theoretical properties are analyzed and empirically compared in a replicable experimental study. The described IS-within-CL schemes yield an entire approximation of the partition function, so enabling a possible efficient Bayesian inference. An optimal independent proposal density for IS-within-CL methods and the GA is also introduced. Overall, this work contributes to a clearer unification of likelihood-approximation and CL approaches, offering both theoretical understanding and practical tools for inference in energy-based and non-normalized models. Related MATLAB and R codes are also made freely available to help the reproducibility of the results.