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NOPAT = EBIT(1-t) which doesn't adjust for interest expense. Also EVA = NOPAT - $WACC which again accounts for profit generated after tax after contributions from all capital sources, debt and equity.

RI model looks at just excess equity returns. Since RI uses Book Value (assets net of liabilities) only an equity measure of profit must be used, hence Net Income over NOPAT.
RI = Net Income - (required return on equity x B(t-1))

The only time NI and NOPAT would be the same is if the company is financed 100% through equity. Then EVA and RI would give the same results.