Strain is a specific technical term. To date there is only one known strain of SARS-CoV-2. There are small mutations, variations, etc that can be used to track the spread over time and place.
One thing I'd add to the travel shutdown (or lack thereof) discussion is that a virus doesn't care about your citizenship. The ban from China didn't include US citizens and permanent residents. Who do you think constitutes the majority of travelers from China to the US?