BC and AD, and BCE and CE are year notations for the Gregorian calendar, which is the worlds most widely used calendar era. The difference between BC and AD, and BCE and CE is that BC and AD directly reference Christs birth, while BCE and CE are more secular ways to tell time. Specifically, BC stands for "Before Christ," while AD stands for "Anno Domini," which means "the year of our Lord" in Latin. BCE stands for "Before the Common Era," while CE stands for "Common Era" or "Current Era".
The use of BCE and CE notation has become more widespread in the later part of the 20th century, replacing BC/AD in a number of fields, notably science and academia. Some academics in the fields of theology, education, archaeology, and history have adopted CE and BCE notation despite some disagreement. Several style guides now prefer or mandate its use. However, some Christian, non-Christian, and non-religious individuals oppose the usage of Common Era, noting that there is no difference in the origin of the two systems. BCE and CE are still based on BC and AD and denote the periods before and after Jesus was born.
Most style guides do not express a preference for one system, although BC/AD still prevails in most journalistic contexts. Academic and scientific texts tend to use BCE/CE. Since both are in regular use with supporting arguments for each, no one system is recommended over the other.