Immigration data varies widely depending on the research question. If working with a small population or a population defined by characteristics that aren't gathered in the census (religion or child of immigrants, for example), consider looking for researcher-gathered data that intentionally over-samples that group, rather than a nationally representative sample. ICPSR is an excellent source for this. Contact your librarian for more support.
Stock data is used to estimate the number of individuals of a certain population of interest at a specific point in time.
For example: The number of naturalized Colombian immigrants residing in the U.S as of July 2023.
Flow data is an estimate of change (addition/subtraction) of a population of interest at a specified period of time.
For example: The estimate of the number of persons arriving to the U.S from Vietnam for the years of 1965-1975.