Why do they use am and pm for time in America and the 24-hour notation in Belgium?

Answer

Interesting question. In fact, we systematically use the twelve-hour clock in everyday language. We say: let’s meet at the cinema at eight o’clock; but we note in our agenda: 20 h. Since the 15th century, watches and clocks with a non-digital time indication have always used a twelve-hour indication that is run twice every 24 hours; in the 14th century, clocks were common that showed the 24 h. of a day, but that was more difficult to read and was supplanted by the clearer division that essentially assumes a morning and an evening. We are also talking about the morning (ante meridiem; AM) and the afternoon (post meridiem; PM).
Conclusion: in the Anglophone world the prevailing system of thinking in terms of before noon and after noon has been adhered to; on the European mainland, the more technical system of division into 24 hours has become common as a writing system, but not as strong as an oral system (although Flemish people in particular will sometimes speak of eighteen thirty to six thirty in the evening).