BC - Before Christ. This is for all dates prior to 2021 years ago. Those dates start counting back up from 1 BC AD - Anno Domini. A Latin phrase meaning "In the year of the Lord". These are for all dates from the year 1 onwards. These forms of marking dates came from Christianity. We also have: CE - Common Era, a nonreligious version of AD. BCE - Before Common Era, a nonreligious version of BC

The Latin terms that historians used for BC were longer, and I guess the appeal of the two-letter acronym was more appealing than using ante Christum natum or ante incarnationis dominicae tempus. Still, nobody used AD before English existed, and it became more and more popular as the years went on, especially as a language of science and learning. In French, it's av-JC for 'avant Jesus Christ', which means the same thing as BC.

BCE/CE usually refers to the Common Era (the years are the same as AD/BC). 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). Wikipedia, Anno Domini article:

For example, Cunningham and Starr (1998) write that "B.C.E./C.E. …do not presuppose faith in Christ and hence are more appropriate for interfaith dialog than the conventional B.C./A.D."

If there is a standardization or shift occurring, it's likely toward BCE/CE, at least in the United States. Common Era notation is used in many schools and academic settings.

If you are going to have a system to describe what date it is you are going to have to chose a point fro which to count on. You can do things like the 3rd years in the reign of some Monarch or similar but that can get confusing really fast. The easiest way is to pick a point in time a count the years since that event. Some monk in the early middle ages decided that he didn't like the systems in use in his time for religious reasons and thought to create a replacement that instead counted the years since the birth of Jesus. The problem was that nobody is quite sure when that was supposed to have been and the monk was working with limited resources. So he picked a year 525 years before his time as the new year 1. The system numbered years since that year and labeled them AD (Anno Domini - "Year of the Lord" in Latin). This new system was mostly ignored for several centuries before people started to adopt it for every day use. Later the system was extended backwards to include dates before the year 1. Those were labeled in English with BC (Before Christ). It is important to note that this backwards extension did not include a year 0. Year 1 BC was immediately followed by year 1 AD. This means that you can't treat a BC value like a negative AD value. If someone were to create a system like that today they would include a year zero, but it was created before modern math ideas had caught on in the west. There are also issues that years didn't use to start on January 1st and that the calendar used wasn't always the same. This can make things a bit difficult when you try to figure out how long ago a date in the past was exactly, but for rough estimates just counting the years works. The BC system is mostly used for things that happened in human history, but not prehistoric events. If you go back long enough you start simply saying x years ago. 12,000 years ago is just a rough estimate and the fact that 12,000 years ago from 1970 is technically a different point than 12,000 years ago from today doesn't matter since the difference is swallowed up by the rounding anyway. If you go really far back to millions of years ago (mya) the whole AD thing doesn't matter because 2000 years become a rounding error on those timescales. We only use AD and BC for things that happened during historical times when there were people who wrote stuff down. We now live in the year 2023 AD which means that the point that the monk calculate Jesus to have been born was 2023 years ago. Thanks to colonialism and imperialism the system is widely used around the world even by people who aren't Christians. To make it more neutral and easier to use and to prevent anyone from coming up with a new system, the labels AD and BC have been replaced in part with CE and BCE (Common Era and Before Common Era). They mean the same thing 2023 AD is 2023 CE and 753 BC is 753 BCE, hey just are more neutral an more palatable for people who have issues with the religious aspect of the name.