Can my family member actually sponsor me, and does the relationship type matter?

Illustrative — not a real business

It depends entirely on the specific relationship and the sponsor's own immigration status, and the difference between categories is enormous, not a minor technicality. If a U.S. citizen is sponsoring a spouse, unmarried child under 21, or parent, that falls under the immediate relative category, which has no annual numerical cap and generally moves the fastest, often within a year or so. Nearly every other family relationship — a citizen sponsoring a married child or a sibling, or a permanent resident sponsoring a spouse or child — falls into a family preference category with an annual numerical limit, and depending on the category and the beneficiary's country of birth, the wait can run anywhere from several years to well over a decade. Some relationships you might expect to qualify simply do not under current law — a U.S. citizen generally cannot sponsor a grandparent, aunt, uncle, or cousin directly, however close that relationship is in practice. Whether the sponsor is a citizen or a green card holder changes both which categories are available and how long the wait realistically is, so that is one of the first things worth establishing clearly in a consultation before any expectations are set.