I won't comment since I know little about the 1920 war. Especially since how it was glossed over in middle school by my teacher and I really need to revise my knowledge of contemporary polish history either way.

The other way around, Poland invaded the areas of the former Russian Empire previously occupied by Germany after the german troops withdrew. Hence the war being called polish-soviet war, the agressor is always first in the common naming convention for wars. The Soviets, not to keen on polish troops on their de jure territories pushed them back, but where defeated at Warsaw. Poland then annexed western Ukraine, western Belorussia and southern Lithuania. The border was then called the curzon line.