They mean: Common Era and Before Common Era which is the equivalent of Anni Domini and Before Christ respectively
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The first century CE began at the beginning of 1 CE and ended at the end of 100 CE. The first century BCE ended at the end of 1 BCE, and the second century CE began at the beginning of 101 CE. (Note that there is no year 0, so 1 BCE immediately precedes 1 CE.)
Remembering that there was no year zero, there were 399 years between 200 BCE and 200 CE.
1 CE was exactly 2,009 years ago. The year preceding that was the year 1 BCE.
1049 years, remembering that there is no year zero.
If by BC you mean before the birth of Christ and by CE you mean Christian Era, then the Christian Era started with the birth of Christ - so BC came first. The link I will place below is an interesting read!