The Russian expansion might perhaps be seen as two seperate (though related) expansions.

The first (and most rapid) was the Russian expansion east across Siberia, north of the Steppes. This started in 1580, and the Russians reached the Pacific in 1639. So, it only took them 59 years.

This expansion was against reindeer herders, hunter-gatherers, living in the taiga north of the steppes.

Here, resistance was less than the American expansion against farmers, who had kept English colonists East of the Appalachian Mountains for 150 years.

There were perhaps two main differences.

The English settlers started off with very small colonies, and took some time to build population and a base to expand from, whereas the Russians started with a much larger population and greater base.

The Native Americans benefited from being able to be supplied with firearms from the multiple European Nations colonizing parts of North America (English, French, Dutch, Spanish) and play them off against each other.

Native Siberians had some support from the Khanate of Sibir (steppe nomads), but they did not get as much support or weaponry as Native Americans did.

The "second" Russian expansion was south and east against the steppe nomads. This was a much harder expansion, which took much longer. This lasted from 1480, when Russia "threw off the Tatar Yoke" at the Great Stand on the Ugra River, until 1783, when Russia annexed Crimea, in a southward direction, and perhaps until 1894, when the Russian Empire made its last territorial acquisitions in Central Asia.

The Steppe Nomads were a more numerous and difficult foe for the Russians than the Great Plains Indians were for the American Expansion. (Both were mounted nomads, though the steppe nomads were herders of domesticated flocks, while the Plains Indians were hunters of wild buffalo.)

The Steppe Nomads had powerful allies (the Ottoman Empire), which supplied them with firearms and ammunition, and also assisted them with troops. The Great Plains Indians had no external allies.

So, the first Russian expansion, across Siberia was from a stronger base, against less numerous indigenous people, with fewer allies, than the American expansion against Eastern Native Americans.

The second Russian expansion across the steppes, was against more numerous indigenous people, with stronger allies, than the American expansion against the Great Plains Indians.