Of course not, but a state is not a country. Germany has 16 states, for example, and the statistics don't count people from different states as immigrants.
However, a person from a neighbouring country (e.g. Mexico) would count as an immigrant in the US.
Just because states are massive in the US doesn't make them equivalent to different countries in Europe, which all have their own language, ethnic background, and culture. A German person moving 350 miles to Italy (from Munich to Venice) is definitely an immigrant, with a completely different background, even though the distance itself isn't even enough to go between Austin and Houston in Texas.
However, a person from a neighbouring country (e.g. Mexico) would count as an immigrant in the US.
Just because states are massive in the US doesn't make them equivalent to different countries in Europe, which all have their own language, ethnic background, and culture. A German person moving 350 miles to Italy (from Munich to Venice) is definitely an immigrant, with a completely different background, even though the distance itself isn't even enough to go between Austin and Houston in Texas.