An expat is someone living outside (ex) of their homeland (patria, technically fatherland rather than homeland if we are pedantic). All immigrants and non-immigrants [1] are expats, by definition, no matter the connotation some people have decided to give the word.

[1] Non-immigrant is the administrative word used by the United States to designate people that are supposed to leave the country rather than settle in the US, usually on training/work/investor visas.