"Europe" is a name of Phoenician origin, much older than Christianity. It was already old when Classical Greece was young.
A lot of the modern confusion stems from the tendency of EU to refer to itself as "Europe" (see: European Council, European Central Bank, European Parliament etc.)
That might be the case in the 1980s, but later I believe another mindset prevailed: an ambition of the EU to actually expand to include entire Europe, or at least the non-Russian part thereof.
With Brexit, the complicated security situation east of Poland and the fact that the Swiss, the Norwegians and the Icelanders seem to be OK with staying outside, this ambition is no longer realistic to fulfill short- to mid-term, but it survives nonetheless.
Realistically, though, Russia would have to change a lot internally before joining the EU.
I am slightly more optimistic about Turkish membership, if Erdogan bites the dust and someone more Western-like (Imamoglu?) comes to power and rewrites the constitution again. Turkish industry is very much integrated into European supply chains.
"Europe from Lisbon to Vladivostok" is a much older ideal, IIRC it has roots as far as in early 90s. And if you stretch it enough you can even trace it back to Charles de Gaulle. But for it to happen not only Russia has to significantly improve internally, but also EU itself has to be different. For starters it would have to be truly independent from the US influence and Brussel's grip on the union would have to be weaker. Russian political culture historically is very firm on being able to independently decide its own fate (and no, it's not a matter of "democratization"). Take the current EU issues with the Poles and multiply it a hundredfold to get a rough approximation of what the current EU would have with Russia.
Before 2007 (see the Munich speech) Russia sincerely tried to join the EU and the collective West. But the condition "proposed" at the time and attitude towards Russia fundamentally collided with that deep culture, resulting in the situation which we see today. If you want to learn more about it from a non-Western perspective, I recommend watching https://www.youtube.com/watch?v=8X7Ng75e5gQ
A lot of the modern confusion stems from the tendency of EU to refer to itself as "Europe" (see: European Council, European Central Bank, European Parliament etc.)