gavra: Agudah constituents in America, Chasidim in America and Yeshivish in America as well as Agudah constituents in Israel, Chasidim in Israel and Yeshivish in Israel would all self-identify as a Chareidi/UO on a survey, if asked. And the aforementioned Americans (the guy on the street, not just the Agudah leadership) would associate themselves with the aforementioned Israelis. Similarly the American MO would associate with the Israeli DL/RZ. Even if in both cases there are some differences, that’s who they would identify with in both cases.
The Chareidi American bochorim go to learn in Brisk (and other Israeli Chareidi yeshivos), not in hesder yeshivos.
When Pew Research did their survey in 2014 of American Jewry, 66% of American Orthodox Jews self-identified on the survey as Ultra Orthodox.
IITFT: The moniker may be somewhat of recent vintage, but the self-identification I’m referring to isn’t anything new. When the Chazon Ish was around, the people in America who are called Chareidim today, their parents back then self-identified with whatever the Chazon Ish’s sociological group was called.