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Are you a resident or a nonresident for tax purposes?
This is not about immigration status. The IRS uses its own test, and it is the answer that decides which tax return you are supposed to file.
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How the test works
Why the answer is not just "how long have I been here".
The substantial presence test weighs years differently
Days in the current year count fully, days in the year before count as a third, and days two years before count as a sixth. Reaching 183 weighted days generally makes you a resident for tax purposes.
Students and scholars get their days excluded — for a while
On an F, J, M or Q visa your days usually do not count at all. For students that exemption lasts five calendar years over your lifetime; for professors, researchers and trainees it is a different, shorter test.
A part of a year counts as a whole year
Arriving in August still uses up a full calendar year of your exemption. This is what surprises returning students most often, and it is why the earlier-years question above matters.