Apparently not--they're also ramping up their defense spending, as if they're afraid we'll pull the same trick on them that they pulled on Georgia. Given that they're asking the EU and not NATO to provide peacekeeping troops, they obviously are afraid that somebody will come after them for what they've done.
It could be that they're right to be worried. NATO has realized that the original threat that the organization was created to contain hasn't gone away. They're putting plans together for a rapid-reaction force to prevent more such Russian aggression against former satellite countries.
Russia's claim that they're not seeking war with us is more of the same: diplomatic doublespeak. They are planning on some conflict--they wouldn't have increased defense spending otherwise--but I doubt that it will be direct. It's more likely to be more of the same type of proxy war they fought against us during the entire first Cold War.
I'm not sure, but I certainly suspect that NATO's plans will never be put into practice. They may believe that the simple existence of rapid-reaction plans will deter Russia from acting against its former subjugated satellites. Once again, more diplomatic doublespeak.
This isn't settling down, and it won't go away if we ignore it and wish it would. We have to react, and react strongly. We're the only ones Russia fears--and then, only they believe we'll carry out the threats we make.