Being a resident and being a tax resident are two completely different things. There are a few Asian countries (I believe Thailand) is one where you only pay tax on income if you're classified as a permanent resident. If you're on something like a 90 day business visa then Thai tax laws don't apply.

Contrast that with somewhere like the UK where you're deemed a tax resident only if you've been resident in the country for >= 178 days in the financial year (regardless of visa status). Combine the two scenarios, carefully managed, you can greatly reduce the amount of tax you pay.

It cuts both ways though. Somewhere like Australia which has a different tax year to the UK and it's possible to incur a tax liability in both the UK and Australia. You'd need to submit a return in both places, thankfully they have a tax treaty with each other to avoid paying double but you'll still need to submit returns to both.

But back to the OP, it's exactly this kind of approach wealthy individuals use to avoid paying taxes. Claim tax residence in a country that only wants your money if you're actually living there, live somewhere else that only wants your money if you're earning it in that country.

US is rare in that it declares the right to tax its citizens' income wherever they live. Most countries don't do that.