Are there major differences if a city grows through local births or migration?

[Capsicum]

Cities can grow through many ways -- births, migration from nearby (e.g. regional, within-state, or province) or out-of-state (or province) transplants, or international migration.

Maybe there are some differences in how family-oriented housing is built or how schools are if local births drive growth versus young adult transplants or migrants, but then again if migrants settle and have kids, perhaps the difference is not as big.

Obviously, there can be major differences in cultural or demographic changes if transplants or immigrants grow the city from farther afield than either local births or local domestic migration (e.g. from nearby towns).

[Yuri]

A city that gets lots of immigrants tend to have a higher birth rate and a higher natural growth, even with a low TFR. Most people who migrate are between 20-45, in their reproductive years.

The two things are interconnected.

[Crawford]

In most developed nations, with high rates of immigration tend to have lower birth rates. Immigrants don't have notably different natality, and tend to flock to high wage, high housing cost metros.

[Yuri]

Low TFR, not necessarily low birth rates. Places that get a large number of immigrants, have a deformed pyramid, with many people on the reproductive age. Even if they have few children, overall this society will have more births.

That’s easily observed on rural vs urban demographics or in the US, even between metro areas (e.g. Pittsburgh vs Dallas). TFR (number of child per woman on reproductive age) might be very similar but as Dallas has proportionally more women on reproductive age, birth rates will be higher there whereas death rates will be lower.