You're right to point out the discrepancy with Dionysius Exiguus' calculation of the birth of Christ. While he intended to establish the year of Christ's birth as the starting point, there is evidence to suggest that his calculations were slightly inaccurate, leading to a discrepancy in dating. As a result, the year 1 AD does not correspond precisely to the actual birth year of Jesus.

Regarding the question about the differences between the BC/AD system and the BCE/CE system, there is indeed more to it than just a religiously-neutral description. Here are a few key differences:

1. Religious Connotations: The BC/AD (Before Christ/Anno Domini) system has clear religious connotations, as "Anno Domini" translates from Latin to "In the Year of Our Lord." This terminology is rooted in the Christian belief system. On the other hand, the BCE/CE (Before Common Era/Common Era) system is intended to be religiously neutral, aiming to avoid favoring one religious tradition over others.

2. Inclusivity: The BCE/CE system aims to be more inclusive and inclusive of diverse cultures and beliefs. By removing explicit religious references, it allows for a broader range of individuals to use a common dating system without feeling excluded.

3. Academic and Cultural Shift: The adoption of the BCE/CE system in some academic and cultural contexts represents a shift towards secularization and a desire for more inclusive and diverse perspectives. It acknowledges that the Gregorian calendar, which the BC/AD system is based on, has become widely used globally and that alternative dating conventions can be utilized.

It's important to note that both the BC/AD and BCE/CE systems refer to the same timeline and are essentially interchangeable in terms of chronological dating. The choice of which system to use often depends on personal preference, cultural norms, and the specific context in which the dates are being referenced.

Ultimately, the BCE/CE system offers an alternative to the BC/AD system, aiming to provide a more inclusive and culturally-neutral dating convention favored in certain academic, historical, and interfaith contexts.
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