In Soviet times Nagorno-Karabakh was a mostly Armenian-populated autonomous region in Azerbaijan. In Yugoslav times Kosovo was a mostly Albanian-populated autonomous province of Serbia.
Armenians fought a war against the Azeris in the early 1990s, and the Kosovo Albanians against the Serbs in 1998-99. Nagorno-Karabakh declared independence in 1991. Serbia’s administration and security forces were expelled from Kosovo by NATO in 1999. The region was then run by the United Nations. It declared independence in 2008.
On the face of it there are plenty of similarities between Soviet breakaway statelets like Nagorno-Karabakh and Kosovo. But there are also many differences. No countries have recognised Nagorno-Karabakh as an independent state, but more than 80 have recognised Kosovo. Western countries emphasise that they believe that the Kosovo case is not a precedent for others.