There is no chronological difference between BC (Before Christ) and BCE (Before Common Era).

They refer to the same year numbering system but use different terminology.

BC is a Christian-centric term, while BCE is a secular, religiously neutral alternative three words that avoids reference to Jesus Christ.

BC (Before Christ) 

Refers to the years before the birth of Jesus Christ.

Based on the traditional Christian calendar.

Still widely used and will continue to be.

BCE (Before Common Era)

These three words refer to the same period of years as BC but without using the word ‘Christ’.

Increasingly used in academic, scientific, and official documents.

Accuracy

The BC/AD dating system based on Christ’s birth has historical inaccuracies and doesn’t accommodate non-Christian histories.

It could be viewed as just sophistry because, whatever the terminology, it revolves around the supposed year of birth of Jesus Christ.

It would be clearer to say xxxx years ago, however, this would require continual updating. In this respect BP (Before Present) is a useful device.

Copiously embedded in historical writings are references to a ‘Period’ stating a range of years/centuries that reference the birth year of Christ – for example “the Dvaravati Period (6th-11th century)”.