When I was a kid, I was always taught to refer to years using BC (Before Christ) and AD (Anno Domini / year of our Lord). That is, BC is usually understood to mean "Before the Common Era" and CE to mean "Common Era," though it is possible to reinterpret the abbreviations as "Christian Era." The simplest reason for using BCE/CE as opposed to AD/BC is to avoid reference to Christianity and, in particular, to avoid naming Christ as Lord (BC/AD: Before Christ/In the year of our Lord). Marking it as the "Christian Era" (or more commonly, the "Common Era") allows the same epoch to be used even though the best calculation for Jesus's birth has changed.
This was in part a response to advice Diocletian received at the oracle of Apollo at Didyma.
But moreover, there is only one letter of difference between the two terms, whereas with BC and AD, the terms are clearly different and I find it easier to distinguish! BCE/CE usually refers to the Common Era (the years are the same as AD/BC).
Most organizations and political entities, for the sake of convenience, have adopted the Western calendar, but "Anno Domini"/"Before Christ" are meaningless terms.
It's just as good as the Nth year of reign of Pharaoh Whoever - doesn't require you to believe in the deity of a particular egyptian Whereas making it "common era" implies that it's the correct one and all the others are wrong.
Archaeologists also use BP - before present - which is confusingly set as 1950.