Poland very much is part of the West, and is actually on course to become one of the richest countries in Europe over the next twenty years as measured by GDP per capita.
Over that same period Europe is projected to become poorer than Asia in gdp ppp for the first time in 500 years. I'm sure I won't be hearing Poles making the case they are actually part of Asia within those 20 years.
The whole west/east dichotomy is an artifact of the Cold War. Countries aligned with the US and Europe are "west", countries aligned with the Soviets (now Russia) are "east".
Nowadays China is taking the helm of "east" from Russia, but either way it's a geopolitical concept and remnant.
At the UN, “the West” officially means the “Western European and Others Group” (WEOG). Poland is not a member, it is a member of the Eastern European Group instead. Of course, many consider the UN Regional Groups to be a bit of a Cold War relic. But still, it goes to show that whether or not Poland is part of “the West” all depends on how you choose to define “the West”
"the West" does not officially mean anything, other than vaguely refer to Cold war sides. This is why it is not a very useful model (like left and right in politics).
Poland is definitely Western aligned, as Japan or Australia, which shows the absurdity of this model.
I think your assumption that “normal people” all use the term “the west” in the same way is highly questionable. Many “normal people” don’t really think about what the boundaries of “the west” are and either don’t have an opinion on whether or not Poland belongs in it, or else have a different opinion from yours.
Yes, both Bulgaria and Cyprus are without any doubt part of the west. Both are even part of the European Union. Claiming that they are not part of the west is laughable. Bulgaria is adjacent to Greece which is also part of the west. Culturally large parts of the Balkans are also part of the west.
You're confusing cause and effect. The West is defined by embracing enlightenment values, democracy, and capitalism. The "East" is defined as those powers that embraced authoritarian rule and communism.
For a while there was legit economic competition, Soviet GDP outpaced the US for a time in the 50s, but eventually the economies of scale and efficiency produced by the capitalist West out-competed the Soviets and won the Cold War.
