While I'm definitely no history expert (neither do I specialise in Eastern European studies and relations) I've always been fascinated by the (obscure and contradictory) history of Eastern Slavs, the Cossacks and the connection between them. What I can say for 100% sure is that in regards to Cossacks (and more specifically, their origin) you'll never get the clear picture or the truth. Part of that has to do with:
- cossacks often being misrepresented in media (especially Western media and historical sources)
- cossacks forming their (first) geopolitical centre in the middle of the Wild Territories (lands that used to belong to Poland-Lithuania but were deserted), hence mixing in with the local non-Slavs and absorbing eastern cultural traditions. Over time this contributed the formation of their ethnically-mixed background (which is also why today's Russian authorities attempt to shoehorn cossacks into a long-running list of ethnicities that live on modern Russian territory)
- political allegiance: while it can be argued over who were the first tribes/people to claim the name "cossacks", what can't be dismissed is that the first group of people to bring cossackdom into the political sphere of Eastern Europe were Ruthenians who lived on the Right-Bank Ukraine under the Polish rule. Initially their ventures to the wild steppes meant growing food only to return to the territories under direct Polish control for the winter. After the local elite began raising taxes, the peasants were forced leave their homes in order to get a little "breathing space" from the oppression (not to mention the attempts by the Catholic church to oppress their core Orthodox religion). That's how the Zaporozhian Sich (Host) came into being. It started as an outpost that was formed as self-protection against the Tatars in the South. After the Khmelnytsky uprising of 1648, the Sich expanded into a quasi-state called the Cossack Hetmanate, although it's official status was brought down by a series of "pacts" between Russia and Poland-Lithuania which divided the territory into the Right and Left Bank halves. Russia unofficially administered the Left-Bank (which was supposedly a sovereign state but in reality it was a Russian vassal) while Poland officially owned the Right-Bank (but its control was quite limited as the cossacks that lived in the right bank were far more rebellious and sought to reconnect with their Left-Bank counterparts). What brought down the Hetmanate is the death of Khmelnytsky, after which the political elite began to fight over power (much like their ancestors from the Rus principalities did 400 years ago). They couldnt maintain an effective foreign policy as they were always stuck between three powers (including the Ottoman Empire and Crimea) that tried to vassalise/divide the Hetmanate, which meant that they had to swap alliances all the time. After a really long history of struggling for independence, the cossack potential for a statehood waned and they began to migrate to other territories, such as the Danube, Don (although they have a complex history as well), the Far East, Volga, Caucasus and Urals, where they were used as military resources by different countries. Some cossacks began to spread Ruthenian/proto-Ukrainian culture wherever they went, while some quickly got assimilated. It should be noted that there were a bunch of hosts in Russia that were either unconnected to the Zaporozhian cossacks or were minimally influenced by them. The thing about the Host in the Zaporozhie is that they were the only cossacks to achieve political statehood. The downfall of the Zaporozhian Host is what caused all these misconceptions people have today. There is Russia trying to create a myth that the Cossacks were a Russian phenomena in general, then there is the Ukrainian eductional doctrine spreading a nationalist idea that all Ukrainians are all descendants of Cossacks and that all modern Hosts developed from the Hetmanate (although indeed Ukraine is a "successor state" to the Hetmanate as they are both Ruthenian countries), and finally, you have some misinfromed westerners who claim various BS, such cossacks being Asian in nature, having Tatar roots, being a separate ethnicity, being the Tsar's special forces and other fantastical fan-fiction. Although to be fair, when i was studying cossacks in my university, there were almost ten unique theories on their origin, but again, its hard to say where the truth lies exactly, as many of those theories directly contradict each other.
As for your actual question, the cossacks relied on the Tsar for protection and political support, while the Tsar gradually began to treat the cossacks less as political allies and more like military assets with limited autonomy. The Zaporozhian Host evolved from an outpost to a state to an autonomous subject of Russia, to a scattered resource pool to fill up the ranks of Russian army and cavalry. Some hosts were allowed to keep their teritorial definitions in exchange for loyal service to the Tsar. Cossack effectiveness in battle goes beyond just defending Russia's borderlands (Ukraine, Caucasus) though - they were once spearheading an assault on Napoleon's capital!