Images from the IMAGE satellite of precipitating protons (SU12/FUV) and trapped protons at 8.5 (MENA) and 33 keV (HENA) are compared during three periods: (1) 12 August 2000 from 1000 UT to 1145 UT just after the peak of a strong geomagnetic storm, (2) 2 June 2001 from 0100 to 0345 UT during the main phase and initial recovery of a weak storm, and (3) 18 June 2001 from 1400 to 1645 UT late in the recovery phase of another weak storm. Some of the features of the precipitating and trapped protons observed in these time intervals have been previously reported for other events, especially the fact that the strength of the precipitating protons and trapped protons do not always correlate. The primary new features are that (1) the fluxes of the precipitating protons and both the 8.5 keV and 33 keV trapped protons peak at similar magnetic latitudes and that (2) the peak in the 8.5 keV trapped protons is usually at the same MLT as the peak in the precipitating protons, while the peak in the 33 keV trapped protons is usually in a different MLT region than the peak of the precipitating protons. Some possible mechanisms to explain these observations are presented, but understanding this behavior should provide stringent tests for models of the Earth's inner magnetosphere.