settled / sedentary
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settled
Living in a fixed place and not constantly moving. Describes a way of life with a permanent residence.
Nach vielen Jahren des Reisens wollte er endlich sesshaft werden und eine Familie gründen.
After many years of traveling, he finally wanted to settle down and start a family.
'Sesshaft' (settled / sedentary) is related to the verb 'sitzen' (to sit) and the noun 'Sessel' (armchair). The basic idea is that you 'sit' in one place and no longer move around.
Einige Vogelarten sind hier sesshaft und fliegen im Winter nicht in den Süden.
Some bird species are settled here and do not fly south in winter.
The adjective is often combined with two verbs: 'sesshaft sein' (to be settled) describes the state of living in one place, while 'sesshaft werden' (to settle down) describes the process of establishing oneself somewhere.
Er ist seit zehn Jahren in Berlin sesshaft.
He has been settled in Berlin for ten years.
You can recognize the meaning from the context. If it is about personal life decisions, e.g. 'Familie' (family) or 'Reisen' (traveling), the modern meaning is meant. If it is about history, peoples, or agriculture, the historical meaning is meant.
Mein Bruder ist ein Nomade, er war noch nie länger als zwei Jahre sesshaft.
My brother is a nomad; he has never been settled for more than two years.
based / resident
'ansässig' and 'sesshaft' both have to do with a fixed place. 'ansässig' describes where someone lives or where a company has its registered office, often in formal texts. 'sesshaft' describes more of a way of life: someone does not keep moving, but lives permanently in one fixed place. In historical texts, 'sesshaft' can also mean the opposite of a nomadic way of life. The words can be confused because both express a fixed place. For an address or a company's registered office, 'ansässig' fits; for the decision to live permanently in one place, 'sesshaft' fits.
Nach vielen Jahren auf Reisen möchte Maria in Hamburg sesshaft werden.
After many years of traveling, Maria wants to settle down in Hamburg.
Die Beratungsstelle ist im Zentrum der Stadt ansässig.
The advice center is based in the city center.