I can only speak about Bucharest as that's the area I know best. From what I see it has a slightly higher GDP per capita than Lithuania, and if you factor in the metro area, Bucharest has the same population as the country.
"And is this meant to imply that standard of living is higher in Bucharest than, say, Vilnius?"
Statistically, it is, albeit by a small margin. There is also Cluj Napoca (Romania's second or third largest city, similar size to Vilnius), also at a higher standard of living than both, but I don't know much about that city. Outside these two, Romania is a wasteland.
Edit: Interesting:
Vilnius is the major economic centre of Lithuania. The GDP per capita (nominal) in Vilnius county was €25,400 (~US$30,000)[285] in 2019, making it the wealthiest region in Lithuania and the second-wealthiest region in the Baltic states.
Almost one third of national taxes is paid by Bucharest's citizens and companies. In 2009, at purchasing power parity, Bucharest had a per-capita GDP of €26,100, or 111% that of the European Union average and more than twice the Romanian average.
So likely Bucharest's GDP per capita is higher by a wider margin.
Edit 2:
The region Bucharest-Ilfov is the most developed region in Romania, with a GDP per capita of 139% of the European average. Bucharest thus surpasses other European capitals such as Athens, where the GDP per capita reaches 92% of the EU average, Madrid (125%), Berlin (118%), or Budapest (102%).
If standard of living is purely defined as GDP per capita, then it makes sense.
I was thinking of "standard of living" as something akin to "quality of life" (which is subjective of course, but here are a couple of rankings placing Vilnius above Bucharest [0][1][2][3]). Also, for someone working remotely, a lower GDP per capita (assuming good infrastructure, low inequality/poverty/crime and corruption, etc. which are true in Vilnius, at least) might be preferable.
That being said, I think the trend for most of these statistics (GDP, HDI) for Lithuania vs Romania (or Vilnius vs Bucharest) seems to favor the former as well.
e.g. Vilnius county went from 0.861 to 0.920 HDI (0.59 delta) between 2009 and 2019; Bucharest went from 0.898 to 0.933 HDI (0.35 delta) in the same time period [4]
Either way you are right, quality of life is subjective. I don't particularly enjoy life here overall, just taxes and the group of friends I have. Romania is far behind central and western europe in terms of mindset, but is nowhere near the low level i thought it was.
"And is this meant to imply that standard of living is higher in Bucharest than, say, Vilnius?"
Statistically, it is, albeit by a small margin. There is also Cluj Napoca (Romania's second or third largest city, similar size to Vilnius), also at a higher standard of living than both, but I don't know much about that city. Outside these two, Romania is a wasteland.
Edit: Interesting:
Vilnius is the major economic centre of Lithuania. The GDP per capita (nominal) in Vilnius county was €25,400 (~US$30,000)[285] in 2019, making it the wealthiest region in Lithuania and the second-wealthiest region in the Baltic states.
Almost one third of national taxes is paid by Bucharest's citizens and companies. In 2009, at purchasing power parity, Bucharest had a per-capita GDP of €26,100, or 111% that of the European Union average and more than twice the Romanian average.
So likely Bucharest's GDP per capita is higher by a wider margin.
Edit 2: The region Bucharest-Ilfov is the most developed region in Romania, with a GDP per capita of 139% of the European average. Bucharest thus surpasses other European capitals such as Athens, where the GDP per capita reaches 92% of the EU average, Madrid (125%), Berlin (118%), or Budapest (102%).
https://rumaenien.um.dk/en/the-trade-council/about-romania