What do Migrants Want?

Human history is a story of migration:

What do migrants want? Opinions vary:

“Settler colonialism is distinct from migration because immigrants aim to integrate into an existing society, not replace it.” Wikipedia/Settler Colonialism

“Like many immigrant groups, Africans are keen to preserve their cultural identity and ensure their children do not replace their traditional values with foreign ideas.” Africa Renewal/United Nations publication

So what is it? Assimilation to the new or preservation of the old? I suspect for most immigrants it’s a combination of the two.

Let’s assume there is such a thing as colonial settlers. How does one know what they want?