  We take ($\mu^\pm e^\mp$) systems and consider the states with quantum number
$J^P=0^-$ as examples, to explore the different contents of the instantaneous
Bethe-Salpeter (BS) equation and its analog, Breit equation, by solving them
exactly. The results show that the two equations are not equivalent, although
they are analogous. Furthermore, we point out that the Breit equation contains
extra un-physical solutions, so it should be abandoned if one wishes to have an
accurate description of the bound states for the instantaneous interacting
binding systems.
