[pavelrub]

Yes - both a secular Zionist Jew in Tel Aviv and a Satmar Jew in the US (both are, by the way, most likely Ashkenazi) would see themselves as belonging to the same broad group of people with shared customs, culture and history - the Jews. This is why we refer to both groups as "Jews".

This doesn't of course mean that their "subjective sense of identity" is identical in its entirety, but that's pretty much the case with every ethnicity.