There exists a systematic difference in the ISC body-wave magnitude (mbISC) - seismic moment (M0) relationship between intermediate and deep earthquakes around Japan. For earthquakes with the same M0, the mbISC for intermediate events is larger than that for deep events by 0.2 to 0.3 units. The mbISC discrepancy is attributed to the depth-distance correction in the procedure for determining the mbISC; a larger depth-distance correction (≈ 0.2) is made for the intermediate events than the deep events, irrespective of station distance. The discrepancy disappears if no depth-distance correction is made. I observe no depth-dependent relationship between the M0 and the JMA magnitudes (MJMA), which make a different depth-distance correction. No significant depth-dependent mbISC discrepancy appears in other regions; for example, around Tonga, I observe larger ISC P-wave amplitudes from deep events than intermediate events, which could cancel the effect of the depth-distance correction. The depth-dependent mbISC - M0 relationship around Japan is observed irrespective of whether the magnitudes are determined using the amplitude data at far or near stations, or whether stations are used in the dipping direction of the slab or not. The mbISC discrepancy for the same M0 cannot arise from local structures, radiation patterns, and station coverages. This is not attributable to the dataset of the M0 itself because no significant depth-dependent relationship between M0 and MJMA is observed.