In the past, historians would commonly refer to dates as either BC or AD. The acronym BC was generally meant to refer to times before Christ while AD was shorthand for the Latin phrase Anno Domini or Year of the Lord.
Today, many people use BCE or CE to refer to historical events. When someone says CE, they are referring to the common era, or roughly the same time period after Christ was purported to exist. The use of BCE is meant to refer to the time that is commonly articulated of as the time before the birth of Christ.
There are two reasons why the shift from BC and AD to BCE and CE has occurred. First, using the terms common era and before common era has less of a Christian overtone, which may be beneficial when talking to those who may have a different religious point of view.
There is even evidence to suggest that the use of BC/AD occurred mostly during the Victorian Era and that earlier Christians didn’t use those terms frequently. Second, there is no way to be sure exactly when Jesus was born. Some believe that he was born anywhere from four years before the common era to seven years into the common era.
The shift from BC/AD to BCE/CE has mostly gained traction among academics and other groups who embrace a more secular view of the world. However, many people understand both uses to describe the time periods, and both may be considered correct depending on the audience.