I arrived in Moscow on Wednesday, but which year I am in is not quite clear.

Is this 2014, or 1980? Am I in Russia? Or back in the USSR? In my hotel room I flick from Russian channels to Western ones, and the word "Ukraine" keeps popping up, but it seems to be two different countries. In the BBC's Ukraine, masked Russian militias are kicking humiliated Ukrainian troops out of their barracks in Crimea. In Russian TV's Ukraine, right-wing Ukrainian extremists are hurling rocks at peaceful Russians - or, in one case, beating up a Ukrainian television director for daring to show Vladimir Putin's speech on his channel. Looks like the East-West cold war all over again.

But this can't be the USSR. In communist days they didn't trust the public to speak on live TV. Nowadays the favourite format on Russian channels is the live studio "debate". But the uniformity of views is pure Soviet Union - the shows are like Dimbleby's Question Time, but with every single member of the panel and the audience on the same side. No balance, no dissenting voice.

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And it can't be the USSR, because the USSR was nothing if not internationalist. Today, the saddest consequence of the conflict over Ukraine is that it is turning two Slavic nations against one another. The wounds are being struck fast and furiously, in words and increasingly with violence, and they will take years to heal.

And this can't be the Soviet Union, because the country has changed beyond recognition in the past 20 years. Moscow is a glitzy, Westernised, cosmopolitan city. People are not slaves to a communist ideology; they are free, they travel abroad, they dress and eat like we do. In the metro they have free wi-fi, and passengers sit thumbing their smartphones - reading the Sunday Herald website if they want.

True, this wouldn't be Russia if there weren't also signs of corruption, even in the clean, tidy, efficient metro. Crooks openly advertise their wares on makeshift posters stuck to the carriage walls (and torn down each night): call such-and-such a number and we will provide you with any document you require - a doctor's sick note, fake hotel receipts, perhaps a fake university diploma, sir, or a false income declaration, whatever you need to hoodwink the authorities.

Russia is a country fighting two sides of itself. On the one hand, the inward-looking, aggrieved, nationalistic Russia of Putin's speeches and the TV propaganda; on the other, the Westward-looking Russia with its modern business centres and eateries. In a branch of the French bakery and cafe chain, Paul, they even greet you with "Bonjour, monsieur", as you step inside from the kind of needle-sharp snowstorm that sent Napoleon's troops scuttling back to France without so much as a glass of black tea. They're really trying. If it wasn't for the climate and the propaganda, this could be "the West".

But it's the nationalism that is most worrying. In grabbing Crimea, Putin seems to have touched the nastiest nerve in Russian society. The president himself keeps his voice calm and level, but his followers have descended into a frenzy of Russian triumphalism and scaremongering. The happiest person around is Vladimir Zhirinovsky, the far-right "joker" who sprang to prominence in Russia's first presidential elections, in 1991, vowing to nuke Estonia and pledging that Russian soldiers would one day wash their boots in the waters of the Indian Ocean. Today he doesn't look like such a joker. His policies are being implemented by Putin.

He has many rivals these days for the title of Russia's number one clown. There goes Sergei Markov, one-time MP and "political technologist" (one of those whose attempts to rig Ukraine's elections in 2004 sparked the orange revolution): America's aim right now, he says, on one of those interminable TV shows, is to get Ukraine into Nato, to pump money into its army, make it a massive force, and then attack Crimea and take it back. Any evidence for that? No-one asks.

I am writing this in a cafe, surrounded by sophisticated-looking people, smartly dressed, deciding whether it's jasmine tea or a double espresso, tapping on laptops or talking quietly … and I don't think they are discussing the heroic feats of Russian commandos evicting Ukrainian marines from Crimea. They are the other half of the eternal battle for Russia's soul, always trying to drag it out of the mire. But at the moment, they are on the losing side.