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.