I ,myself, never thought about a distinction until I came across a few uncommon books by engineers criticizing aspects of the Scientific community; and even some of the methods employed by scientists; and especially the pecking order; that opened my eyes.
Prior to that, I had grown accustomed to thinking of engineers as “employed scientists” – or “mere technicians” but I was quite wrong.
Science gets the credit when something goes right. The engineers get the blame when something goes wrong.
You could use Engineering methods to do Science; a lot of science has come out many a philosophizing Engineer, who afterwards was labeled a Scientist. But there seems to generally be a humility among Engineers; perhaps because they are typically working for somebody else who pays for the equipment, etc – so its rare to hear of a famous Engineer; but common to hear of a famous Scientist.
Science could be used to do Engineering; although the process may take longer, as sometimes things get blurred in Science (the classic example of the “spherical horse” – it’s a joke among Engineers about Physicists) – and precision isn’t always necessary for a decent hypothesis to become a working theory.
Mathematics fills in the gap quite often; just as it has been useful in Engineering, it is also useful in much of Science. (not all of science always benefits from mathematics; often language serves a similar purpose, with more flexibility in some areas yet some weaknesses in others. (math is compact and has the potential to be quite precise up to whatever is considered an acceptable stopping point – language can be more ambiguous but has greater flexibility, as all math can be described by language, but not all language can be described (yet) by mathematics).
In all cases, though, they are all about transforming ideas. Mathematics is sometimes romanticized (note the recent book where the author considers the WHOLE UNIVERSE to be mathematics – a good example of the tool becoming an object of worship) – and Science often is as well; but I don’t know too much glorification of Engineering. It’s hard, it has to be as correct as possible, the education is brutal because so many fields have to come together… and.. especially in the case of structural engineering, you can’t have someone walk on your bridge and die; so engineering tends to approach things from a “least failure” perspective rather than hypothesis and theories.
And yes, they’re different. I’m not knocking science, although I seem to be. I’ve just noticed a trend in my life of a glorification of science (mostly that of theoretical physics, which has enjoyed the spotlight since the 20s + Einstein became such a celebrity; but even BEFORE that with Michael Faraday and his famous Christmas Lectures.)
I got caught up in it for about 10 years; and I’m not abandoning it; just changing my perspective to that of a metaphorical one; “Where mathematics comes from” is on my reading list, although seeing Science as a modern (but practical) mythology in the style of Joseph Campbell isn’t much of a stretch; it doesn’t take away from its usefulness viewing it as a mythology; but perhaps it can take a little of the worship of its perfect-results-when-done-properly idealism.
Idealism itself is flawed anway; we’re not brains-in-vats envisioning perfected forms, but humans whose brains are like a gooey olive-oil structure which contains many nerve endings, integrating with society through mirror neurons and self-integrating through the memory of the forms patterned from the various movements of the body and abstracted within the brain itself (a physical system).
Eh, I’m babbling; sorry