Colonization is used to describe an act that would otherwise be called “waging war,” except that the people subjected to this act do not have an army with which to resist. If the people you are trying to “colonize” have a functioning state with a functioning army with which to keep you out of their territory and pilfering your natural resources, then that’s what they’re going to do.
Before the modern notion of what we call ‘nation-states’ emerged, societies fought and conquered each other all the time. We don’t call that ‘colonization’ because the idea of having a colony just wasn’t in the cards, colonies require power projection, when you can use the threat of military action to ensure subjugation. Without power projection, you had to literally administer provinces, always within easy reach of your army. We call this empire. The size and reach of your army limits how big you can grow, along with the size and organization of your dominion.
And so Russia was an empire starting from Peter the Great in 1721 to its dissolution in 1917. Russia lasted a surprisingly long time as an empire. Most empires of Europe and the West started breaking up into nation-states in the 1800s. Empires were multi-ethnic, nation-states have one predominant ethnicity.
It’s the ethnic part that really makes up the meat of the meaning of the word ‘colonization’, so we generally use it to refer to when a nation-state exerts political dominance over another ethnic group. We don’t really say that Russia had colonies, because it was an empire, it’s already multi-ethnic, any ‘colonies’ would just be additions to its empire.
You can’t colonize an empire, you can only conquer it, in parts or in whole. A piece of the Russian empire, Manchuria, was pulled off by Japan, and World War I saw Russia lose its claim on Finland and the Baltics.
Other than that, colonization can also refer to the settling of unoccupied land. The United States successively colonized its current territory over perhaps a hundred years. Dima Vorobiev describes it better than I could.