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Zolkiewski's army had an equal amount of Poles and Zaporozhian Cossacks (10k each) aided by Ruthenian army led by Lew Sapieha and German and Hungarian mercanaries. This multi-ethnic organization won two big battles under Smolensk and Klushino. At that point the Russian state in the middle of a civil war stopped functioning and the remnants of this army (just 3000 men) entered Moscow without a battle. When they actually had to fight for Moscow, the commander in chief was Jonas Chodkevicius from Vilnius and the bulk of his army were Cossacks.
Polish-Lithuanian commonwealth can be summarized as a pact where Lithuania had to aid Poland in their wars with the Germans, and where Poland had to aid Lithuania in their wars with Muscovy/Russia.
If you are able to see the broader picture, the conflict starts in 1300s when a small Baltic tribe went on a power trip, conquered several Slavic principalities in what is today Belarus and Ukraine, and later used them as a cannon fodder for their further conquests, trying to subjugate Upper Oka Principalities in the vicinity of Moscow no less. Eventually the Slavs felt like they "belong" in this country and willingly fought the wars against Moscow. As long as the Slavic country of "Lithuania" was faring well in their conflict with Moscow, they were not interested in a union with Poland, but the balance of power inevitably shifted in favor of Moscow, and the Slavic country of "Lithuania" was unable to secure its possessions without the help of Poles who themselves needed a strong ally in their conflict with the Germans.
https://en.wikipedia.org/wiki/Muscov...cal_background
The conflict lasted for centuries with periods of temporary peace, and in the second half of it, the Poles were dragged into it to defend the interests of a Slavic country "Lithuania".
A bloodbath in which ancestors of Russians, Belarusians and Ukrainians were killing each other is in no shape or form a conflict between Orthodoxy and Catholicism.
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