A comparison between noise-induced synchronization and master-slave (Pecora-Carroll) synchronization is investigated in this paper. We find an interesting correspondence between the effective driving variables of these two kinds of synchronizations in three-dimensional chaotic systems, when the systems have nonlinear terms in more than one equation. A study of the Lorenz model, the Hindmarsh-Rose neuron model, and the Hastings-Powell foodweb model is given to support this claim. It is a somewhat surprising result since these two kinds of synchronizations arise through different mechanisms. We also examine an exceptional case, where the nonlinear term of the system appears in a single equation, as in the Pikovsky-Rabinovich circuit model, and explain why the correspondence fails.