"Beauty" is something I cannot define. "Elegance", as I use it, is the use of tools as precisely as possible. It is a technical term, whereas "beauty" I cannot define.

Of course, that is my view of it.

Maybe English isn't your first language, but these are basically synonyms.

Maybe English is also not your first language, because they are not synonyms

When writing code I also believed in the "beauty" and "elegance" because IMO it opens up all kinds of different opportunities that involve using or organically growing or improving that code. It turns out that if it doesn't solve a quantifiable problem, (mostly) nobody cares. And the pace of innovating in the field outgrows the pace (by a large) of keeping things "beautiful and elegant".