The story
Originally with reference to the separation of the Czech Republic and Slovakia in 1993, by analogy with the Velvet Revolution (Czech: sametová revoluce) of 1989.
Etymology from Wiktionary, CC BY-SA 4.0.
velvet divorce
Today it means: A non-violent separation of formerly united nations, especially the one which occurred when Czechoslovakia split into the Czech Republic and Slovakia in 1993. Full definition →