In US -> Fancy dress-> tux and the like
"formal"/"dressed up"-> jacket and tie
"semi-formal"/"dress casual"-> button down (no tie), sweater, polo

VERY seldom are tuxedos worn at all over here, unless one is fairly well off/rich. Few own them and most rent them. Basically, most wear them for prom, weddings (wedding party itself-> groom and groomsmen only), and the occasional fancy dress ball (which most NEVER attend at all).

A nice tweed jacket will worn for 99.9% of US "dress casual" and up occasions. In some of the others, it would also pass (as you undoubtedly NOT be the lowest dressed person in the room).

I know quite a few people who only own 1 or 2 ties and not even a dress jacket at all. They find no need for them in their life.

A charcoal tweed on a "nice" cut would be a good buy.