Good question. As with everything else, it depends how you look at it. The first definition is closer to the general consensus right now, and very well put: an interface between humans and AI. The second definition is to emphasize that it's not necessarily different in kind from both code and natural language but different in degree.

The idea that prompt engineering, using a broader definition, is a spectrum that includes code and natural language at the extremes is useful to understand the relationship but may not hold up against some definitional criteria (e.g., it seems that natural language follows a universal grammar, which is beyond PE, so in that sense I shouldn't say they're not different in kind)