In this paper, hybridizable discontinuous Galerkin (HDG) methods using scalar and vector hybrid variables for steady-state diffusion problems are considered. We propose a unified framework to analyze the methods, where both the hybrid variables are treated as double-valued functions. If either of them is single valued, the well-posedness is ensured under some assumptions on approximation spaces. Moreover, we prove that all methods are superconvergent, based on the so-called $M$-decomposition theory. Numerical results are presented to validate our theoretical results.