Empires, puppet states, colonies, and territories are mostly pre 20th century relics today, and we've lost the vocabulary for talking about them. Pundits still throw those words around, but mostly as exaggerations.
This is a 19th century war with 21st century weapons. It's from the bad old days when various European states built empires - the Austro-Hungarian Empire, the British Empire, Imperial Russia, and the Imperial State of Germany. For most of the 18th and 19th century, and up to WWI, there were wars around the fringes of those empires. Not hugely destructive ones, because nobody had enough firepower.
Putin seems to want to go back to that era. Not, as some people think, to the USSR era. Read that accidentally posted Russian victory press release.[1]
It's a good time to look at 19th century European history and the runup to WWI. What's happening is all too similar.
[1] https://web.archive.org/web/20220226051154/https://ria.ru/20...