Some cultures that worshiped the moon like lunar calendars (ancient Arabs and Persians) while Sun worshipers favored solar calendars (Romans). Their pagan preferences live on into today.
When Pope Gregory XII recommended his new calendar most Catholic countries and some Protestant Dutch provinces followed suit. Other Protestant countries rejected the more accuarate calendar because it is a Catholic, Papist invention. It took the United Kingdom and its colonies until 1752 to start a transfer over to the Gregorian calendar (however the tax calendar, based on the Julian, only was align in 1900). British citizens rioted against the new calendar because they though the Pope stole time from their lives. Such were the anti-Catholic feelings back then.
The Julian Calendar continued to live on in Eastern Europe. Civil affairs there were either handled by Russia or the Ottoman Empire (which used the Muslim calendar but allowed for Orthodox churches to use the Julian). When the Balkans became free efforts were launched to Europeanize the countries and that included adopting the Gregorian calendar. Russia adopted the calendar under the Soviet October Revolution (which occurred in the Gregorian month of November). Greece was the last Eastern European country to switch in 1923. The Orthodox Churches though refused the Catholic invention. So some adopted the Revised Julian Calendar which just so happens to be almost exactly the same as the Gregorian. Some Greek Orthodox thought changing the way the church sees time to the Roman way to be heresy and broke off. Today these groups are known as Old Calendarists.
The Gregorian Calendar like the Julian is centered on Christ's original assumed birth date. B.C. comes after the date and means "before Christ" while A.D. comes before the date and translate to "In the year of Our Lord." Some academics prefer B.C.E "before current era" and C.E. "current era" after the date in an effort to secularize time.
Fighting God in time is not new in Europe. The French Republican Calendar was the pride of the French Revolution. It featured 10 day weeks, 3 week months, 12 months, and a series of special quasi-holidays to fill in the rest at the end of the year. The days were named first day through tenth day and instead of Saints each date was given a fruit name. The calendar started on the Gregorian September 22, 1792 - the date of start of the French First Republic. The calendar lasted thirteen years. The Soviet tried something different after tinkering with the Gregorian calendar. The Soviet Revolutionary Calendar had 5 day weeks, 6 week months, 12 months, and a series of holidays in between. Each day was given a color to correspond with a worker's day off. The calendar lasted in one form or another for about 11 years until 1940. The Soviets lost out to the Orthodox tradition of Sunday being a day of rest with workers taking that off as well.
Other Christians mark time in unique ways. The Copts of Egypt use the ancient Egyptian calendar reformed and sinked in with the Julian calendar by Roman Emperor Augustus. The calendar starts in the Greogiran/Julian year of AD 284, the year Diocletian became Emperor. His reign was marked by tortures and mass executions of Christians. The calendar dates are marked with A.M meaning "After the Martyrs" or "Year of the Martyrs."
Other groups mark time since creation like the Hebrew Calendar of Judaism. Muslim instead mark Muhammad's exile from Mecca. Both these calendars follow the lunar cycle just as their long dead ancient ancestors of Sumeria and Arabia did.