Is it still the case that you have to pick one or the other to recognize?

My understanding was that the US, for example, doesn't recognize Taiwan because it would mean losing trade with China; and that if a country recognizes Taiwan, it loses the ability to trade with mainland China, but gets various benefits from Taiwan as well as easier trade terms.

Of course, it's likely that this has changed; my information is probably a few years out of date, maybe a decade or two.