Edit: go look at the other two top-level comments. They go into a lot more depth. I intended for this one to be a bit of an introduction to the way Russians thought of their Siberian empire, and they provide more specific details.
Sort of, but not exactly. It was still an empire in every sense of the word, but it was different in its own ways too. There are differences in the nature of the relationship between Russia and its subjects compared to European colonial relationships, but they are subtle.
The conquest of Kazan and Astrakhan in the middle of the 16th century is the moment when Muscovy really comes out from under the Mongol shadow and, in its view, asserts itself over its old masters (Kazan and Astrakhan being Muslim heirs to the Golden Horde). But at this point, that view of the relationship was not mutual. Russian "conquests" were finalized with what they called a shert', a borrowed Turkic word they used to mean "peace treaty". But the word was alien to the people the Russians made peace with too, and they interpreted to mean a mutual pact.
Russians thought that their Siberian subjects were paying them yasak (meaning roughly "tribute", but kind of like "tax" too). Siberian peoples would bring local Russian officials rich gifts of furs or other goods, and be greeted with a feast, or with the "sovereign's compensation". So is that an equal delegation bringing gifts as a sign of good faith and being given the gift of a feast in return, or is it a subject people paying tribute? The Siberian peoples seem to have thought it was an equal trade relationship, and only the Russians thought they were making subjects.
But what does that tell us about the international comparison? French fur traders in North America make an interesting parallel. They too asked for furs, and traded for them rather than just taking them. But the French knew that they did not yet rule over their indigenous fur suppliers. The Europeans only considered themselves to be colonizing when they had pushed the original inhabitants off the land, as in present-day USA/Canada, or completely subjugated them into slavery, as in what is now Latin America. I am not an expert on that, though, and since I don't want to go too far and accidentally reinforce the false narrative that the European conquest was suddenly a fait accompli, I will leave it there and go back to Russia.
One surface-level similarity between European colonization and Russian expansion is religion. Converting the natives was seen as vital, and as a way to make them more civilized. Russians explicitly looked to Catholic missionary work and felt that they needed to step their game up in comparison and be more aggressive proselytizers. But not exactly in the same way as in African missionary work, for example.
The boundary between Russianness and non-Russianness was much more porous, because religious conversion was the key deciding factor in Russianness. I don't want to overstate the case: converting did not immediately grant a Siberian person full access to all of the privileges of being Russian. But relatively quickly, within a generation or two, Siberians could become Russians, through Orthodoxy. Converting in the Americas or Africa certainly did not make indigenous peoples into Europeans, not without extensive intermarriage to supplement it. The tension at the heart of European civilizing work, of trying to make "them" into "us" but never too much like us, that tension was there in Russia too, for sure. But the fear of making "them" too much like "us" was always much less pronounced.
Ultimately, what I'm trying to get at, though, is that the difference between "us" and "them" was never as pronounced to start with, though. I would go into a little more detail myself, but Willard Sunderland says it very nicely, and I'm tired, so here's a quote.
The European steppe as a whole was never described as a colony, presumably because it was not geographically separated from the rest of the state, although in other respects — most obviously, the name of New Russia — the implication of a colonial status seemed clear. The inherent ambiguity of all this revealed a basic truth about the steppe that would not go away: at once different enough to demand exploration, dangerous enough to require the settlement of Cossacks and the rule of military viceroys, un-Russian enough to be conquered and appropriated, but still remote enough that it could seem to people in Petersburg as ‘all but bordering China,’ the steppe was not, for all that, defined as a region wholly distinct from Russia. The Russians thus began the most intense period of steppe colonization by invoking much of the rhetorical style of European colonialism yet without clearly identifying the colony in question as a colonial place.
And that may seem like nitpicking, and it kind of is. But it's important because it tells you how Russians interacted with their colonized peoples. Neither Sunderland nor I want to nitpick ourselves away from the fact that this was a colonial empire, and one quite objectionable in many ways, just as the ones in America and Africa. But it was an empire where the boundary between colonizer and colonized was blurrier than in European empires on either of those continents. As Alexander Morrison puts it, "these are differences of degree, not of kind".
If you have any follow-ups about specific regions or times, I would be happy to answer them too. I have been very scant on specifics, and in particular there's a lot to be said about the Caucasus, where Russian expansion was at its most violent, that I did not get into here because it would run on too long.
Sources:
Morrison, Alexander. "What is ‘Colonisation’? An Alternative View of Taming the Wild Field". In No. 4 Forum for Anthropology and Culture.
Khodarkovsky, Michael. "Ignoble Savages and Unfaithful Subjects: Constructing Non-Christian Identities in Early Modern Russia." In Russia's Orient: Imperial Borderlands and Peoples, 1700-1917, eds. Brower, Daniel R., Lazzerini, Edward J. Bloomington: Indiana University Press, 1997.
Slezkine, Yuri. "The Sovereign's Foreigners: Classifying the Native Peoples in Seventeenth-Century Siberia." Russian History 19, No. 1/4, 1992.
Sunderland, Willard. Taming the Wild Field: Colonization and Empire on the Russian Steppe. Ithaca: Cornell University Press, 2004.
I wrote an answer that touched on this a while back, though I looked at Russian expansion into the Caucasus as a source of literature (romanticized ideas of taming the frontier and those who lived there).
Like I noted there though, I can't speak for Siberia and Central Asia as a whole, but I don't think they were seen in the same light:
There are some big parallels between the Russian conquest of Siberia and Central Asia and European colonialism. Often the Russian state very explicitly made these comparisons - native Siberians were often referred to as "Our [American] Indians", and the 19th century conquest of Central Asia was compared to the French conquest of Algeria and Indochina.
A few answers I've written:
This answer talks about how conquest and disease impacted native Siberian populations.
Here is a comparison/contrast between Siberia and the "Wild West".
This is a brief discussion of how Central Asia compared to contemporary colonial projects.
Here is a more in-depth discussion of how Russian conquest, specifically of the steppe areas, unfolded between the 16th and 19th centuries.