Omnisexuality is defined as an attraction to persons of any gender identity (incl non-binary), but gender does still matter for an omnisexual (so in my case for example, I'm attracted to everyone, but more strongly towards men and less towards non-men). Bisexuals are attracted to men and women, but could also be attracted to non-binary people (but not necessarily I think).
So I'd say there's very little difference between them, if any. It's more of a vibe-based thing, whatever label you like the most.
Here in Estonia you'll get asked what kind of tea (black, green etc) you want (restaurants here usually have several kinds of it). It's assumed you want hot tea unless you specifically ask for iced.