What was the difference in the fate of the Slavic peoples who adopted Catholicism or Orthodoxy?

The bottom line is that the Slavic peoples who adopted Orthodoxy found themselves under the protection and influence of Russia / Byzantium. At the same time, countries such as Lithuania, Poland and others found themselves under the protection and influence of the Pope, that is, the Catholic Church. This largely determined their role in the geopolitical arena. So, for example, Poland could fight in an alliance with several European countries against Russia also for the reason that their religion is different.