I'm curious what is about this question. And why it is written "Sweden vs Russia", as despite of Russia the whole Northern League (Denmark-Norway, Russia, Hannover, Prussia and Saxony) fought with Sweden. Polish-Lithunian Commonwealth joined war after 4 years from the beginning of it (war started in 1700), but still it was a bit complicated.

Sweden invaded PLC. Then with some pacts with Sweden, was created Warsaw Confederacy which purpose was to detronize the king. In response, against Sweden was created Sandomierz Confederacy. For five years Poles were fighting with themselves, but eventually they were with the Northern League. And I see it as a rational decision.

Of course in the same century two members of "our" side wanted partitions.

Well because Sweden and Russia were the two countries that initiated the war and like you said Poles were on both sides of the conflict. Either way it's just interesting to see opinions.