You can have two similar engines with different power outputs (forget about bhp, just think delivered power) if one has been fiddled/tuned/set up to use more fuel or, if one has had some fancy work done to it such as balancing, porting, exhaust work etc etc.
Two identical engines will have extremely similar power delivery, so if the one delivers more than the other, they are not similar. Similarity is not only defined by engine size. Typically, a company will have three variants of say, it's 1.9l engine ranging from 74kw to 115 kw. It is not just about engine size but also about fuel delivery, engine management and inlet/outlet port differences.