The difference is that one can do software engineering without much "explicit" math and without resorting to gut feeling (though admittedly much is written on gut feeling too).

By "explicit" I mean that e.g. a lot of things I work on for example certainly will use principles that you could write out formally using various mathematical disciplines, but I may or may not have been aware of the underlying maths when writing it, but that does not mean I'm not approaching it in a systematic way.

In a lot of CS papers, even, the use of maths often turns out to be less formal than code, in that I often see maths used to handwave away details you can't get away with not presenting if writing it out as code.

You could build a bridge with gut feeling, but if you wanted a stable bridge with the least possible material then you have to use math. In most software engineering cases, I guess having an abundance of resources lets us get away without math