People leaving are emigrants. People entering are immigrants. Expat is just a word to whitewash the immigrant label. I say this as an american emigrant who knows “expats” in my new home country.

To the UK they are emigrants.

Expat is a casual term referring to someone whose employer sent them overseas on a posting. Diplomats are the most obvious example, but companies will use the same employment structure.

Different jurisdictions have different official terminology for this type of migrant worker, but their legal status in the host country is typically different to that of other categories of migrant worker in the same country, they are usually paid & taxed in their home country, and employed under the regulations of their home country (though in some instances, a host country may extend protections or impose obligations over them).

The confusion arises because when the UK had an Empire, huge numbers were sent abroad to run it, whether for companies like the East India Company, or as civil servants or on military postings, and so the British now think of "people who live abroad" as "expats" because that's the word the older generations always heard, and then continued to use long after this ceased to be the predominant vehicle for of British to be living outside the UK.

The word is absolutely couched in a colonial past, but those using the term to describe other types of British people overseas are not generally doing so out of some sense of white supremacy or British exceptionalism, but plain old lack of awareness.