The empirical works demonstrate that wealth distribution and income distribution have very similar characteristics. This fact makes some researchers fall into a confusion of the two distributions. As important economic variables, wealth and income are quite different in both concept and measurement. These differences should be recognized and embodied in the process of modeling and simulation. Taking the explicit definitions of wealth and income into account, this paper illustrates that income distribution is different from wealth one based on money exchange models. The numerical simulation results show that random exchanging with different trading rules exhibits different types of wealth distribution, but yields almost the same profiles of income distribution.