Well, they weren't really organized at that point. They were a loose collection of semi-independent principalities, but their religion, language, and culture were quite close to each other.
One thing about Russian history which was considered a major turning point (and always kind of bothered me personally) was the story of Ivan IV (The Terrible) killing his own son in a fit of anger. There's a famous painting depicting that event, and the look in Ivan the Terrible's eyes is kind of haunting. An angry, brutal man killing his son in a fit of rage, but didn't really mean to kill him. He had this look of "what have I done" on his face, genuine guilt and remorse. In a way, it kind of symbolizes Russia as a whole. In reality, it was a pretty dumb thing to do, because the only remaining heir to the dynasty was a sickly child who didn't survive.
So, that's what led to the Time of Troubles when the Poles tried to make a play and take over Moscow. That may explain some things about why the Russians had a bit of a grudge against the Poles. But Russia didn't really start to take off until the Romanov Dynasty was established. Prior to that, it was really kind of a disorganized mess in that part of the world. The Romanovs established Russia's position in Europe as it grew to become in modern times.
Sure, the stories of Kievan Rus and the stories of old Muscovy might be somewhat puffed up and mythologized, just as any country might do. Of course, a lot of it has also come from church history. That's another part of the puzzle which doesn't get mentioned as much, as there appear to be some religious underpinnings to this conflict as well.