short answer, no there won't be a war between NATO and Russia. Russia knows it loses no matter what -- even in the economic arena their economy will implode if the US presses for cutting Russia off from the globalized economy. Russia is making calculated power plays in a region they have typically dominated since the renaissance. They need to do it before that region is sucked into the west's sphere of influence like other former satellites and while the west is, comparatively, politically and economically weak (sound familiar? :p).

We mainly view this through the prism of the cold war but I think it's important to understand the relationship between Russia and the west in the post-Soviet era. Think back to the 90's and NATO moving into former Warsaw Pact nations (multiple conflicts in the balkans, initial NATO expansion in Poland+Czech Republic + Hungary) where Russia wasn't in a position to really have much push back.

Then after 9/11, the Russians worked closely with the US on their war on terror -- mainly aiding the Northern Alliance forces to fight the Taliban in the early days of the Afghan war. Then NATO expanded to include countries on Russia's border while the US continued to act with impunity and do brash things like invade Iraq and bomb Libya. When Russia stretched it's military muscle in places like Georgia and Chechnya where their real, local interests were "threatened" the west criticized Russia.

So combine that general political situation with a leader like Putin who wants to restore some of Russia's glory and doesn't mind taking calculated risks or using misinformation to mask a covert war and it makes for a volatile mix. The bottom line is that Putin wants to rebuild Russian greatness; not destroy his nation in a war they will most certainly lose. To me, this feels more like a situation where they wanted to get their strategically important Crimea bases under their control and leave Ukraine in a mess for others to clean up if they won't play ball with Russia.

The fact that sanctions reinforces the narrative about the importance of the Eurasian Economic Union as a way to get off the US-centric system in place today is probably the bigger domestic driver than territorial expansion now that Crimea is firmly under Russia's control and isn't really being contested.