Originally written in 2021-09:
I think "hackers" don't think they are "breaking" stuff but rather that they are "using" it in different ways, enabled by their advanced understanding of the thing in question. For example lock picking isn't breaking and entering, but "using" the locks in a non-designed manner which makes it interesting. They say "if you didn't want your lock to be used this way, why did you design it so to allow it?" They genuinely want things to be fixed, even though broken things are a requirement for their work.
In computer programming, "hack" is then something that "can be done", but probably "shouldn't be done". Such hacks are shunned because, like with locks, non-designed use is more likely to cause unexpected breakages. I don't really think there's a difference between and an engineer and a hacker, but that historically the engineering disciples may have had less room for experimentation as everything was so expensive or important (eg bridges and vehicles). Hackers emerge alongside consumer products, usually electronics.
However, I think there is considerable overlap between hackers and creators (Paul Graham wrote something similar). Sometimes just clever combining of things can be thought of as hacking, even though it's really closer to creating. But at the same time many creators come up with new ways of using their tools, which is my above definition for hacking.