It would only matter when somebody released add-on with both bump and normal maps for the same texture at the same time, but why would they do it (I think it would be rather released with separate normal+displacement or just the bump map)?
Displacement map == bump map == height map. There is no real need for both normal and bump maps since latter contains all information necessary to calculate the former. The only case that comes into my mind is when normal map has much higher resolution than bump map and so it conveys even more higher-frequency details... But this doesn't make a lot of sence from space conservation point of view since bump map uses only single color channel while normal maps are required to have at least two channels. So instead of lower-resolution bump/displacement map + higher-res normal map you could just have higher-res height map...