The article you linked to says the result of the war was Finland ceded land to the USSR. It's a strange war that ends with the Victor ceding land to the defeated.

It's also a strange idea that a fully mobilized Soviet Union in 1945 could push the German army back to Berlin, but would be incapable of taking over Finland. Finland was there for the taking for the Soviet Union in 1945, but the USSR did not see any threat outside Karelia so did not pursue this. This would not have been much disputed at all back then.

They were trying to take all of Finland but got their asses handed to them, taking barely any land and then giving up. A winter war in thick forests against an army of snipers was apparently very different than a tank and infantry war on a flat plain.

You are confusing 2 events. It's true that the USSR almost completely failed their first invasion of Finland. Though for reasons that are much much more complex than simple terrain imo.

But after barbarossa, Finland then seized the opportunity to regain it's earlier losses and attacked the USSR, this time with german help.

That didn't turn out well for the Finnish, and their situation was extremely dire by the end of WW2. Which is why they sued for peace in secret. The USSR could have taken the entirety of Finland at that point, and in fact the finnish government basically evacuated the capital. Why didn't stalin go for it? I guess we can't really know but from the wiki article:

"Stalin's desire to crush Hitler quickly and decisively without distraction from the Finnish sideshow" concluded the war.

Not only that, but for decades after the war, the Finnish communists (puppets to the kremlin) became extremely powerful politically. Finland was forced to hold trials against its own army, and for a time was completely subservient to the soviets. So if they really wanted to take over the entirety of Finland in 1940, I don't see why they wouldn't have done it in 1945.

I'm not confusing anything but you're certainly muddying the water. The USSR lost the Winter War. Period. It's well known and not remotely controversial. They intended to conquer all of Finland and failed. The end. Soviet losses were 5 times greater than Finnish losses. The whole thing is what made Hitler believe he could succeed on what became the Eastern Front.

I totally agree on that. The USSR was completely halted and lost in a humiliating war. There's no debate here, and the insane Soviet losses speak for themselves. What I was saying is that it's still not really clear if Stalin actually wanted to take over Finland. Or just thought he could easily steamroll them and take the territory that was in dispute.