This rule is not common to all countries.
国際的 means 'international' and focuses on relations between nations, while 万国共通 emphasizes something being the same across all countries.
普遍的 is more abstract and philosophical, meaning 'universal' in a timeless or absolute sense, whereas 万国共通 is more concrete and often used for practical, cross-cultural commonalities.
Compound of 万国 (all countries) and 共通 (common, shared). The exact historical derivation is uncertain, but the word is a straightforward Sino-Japanese compound.