"The Zaporojie Cossacks signed a treaty with Russia in the mid-17th century that effectively gave Russia dominion over a large part of what is now Ukraine in exchange for protection from the Polish-Lithuanian Commonwealth. Cossacks also helped conquer Siberia and the mountainous regions of the Caucasus."

You took one part of the history and tried to make it a rule. The Cossaks originated out of Ukraine and moved into other regions, to the Don and to the Kuban and Terek. Further north to the Volga and eventually Ural and then Siberian hosts. Russia had different relationships with each host at each time but they were all Cossacks. And all originating from the same source.

Catherine the Great moved Ukrainian Cossacks from Dnipr (Zaparrojia host) to Kuban as she didn't want such a group in the middle of her Empire. Later Don and other Cossacks joined the Kuban host too. This group, to this day speaks a dialect 70% Ukrainian(I speak it too) expanded Russia to the south and also gave a signifciant contribution to the White and Green Armies.