Tax residency is separate from your visa or citizenship. It's the test a country uses to decide whether it can tax you, and on what. Most countries treat you as a tax resident once you spend 183 or more days there in a year, or once your 'centre of vital interests' — home, family, main economic ties — sits there.
Becoming tax-resident somewhere usually means that country can tax your income; whether it taxes only local income or your worldwide income depends on its system. You can sometimes be tax-resident in two countries at once, which is what tax treaties exist to untangle.
Why it matters for your move
Where you're tax-resident is often the single biggest financial consequence of a move — bigger than rent. Knowing when you'd trigger it (and where) is the first thing to model before you go.