BP Totty
There’s a lot of mini categories in all the 4 categories. You may be technically right that there are 4 general categories but that tells you nothing because there are so many subcategories. If you say someone is Chassidish you know NOTHING unless you ask a whole lot of other questions.
Ill talk about the men. Just a few examples, there’s a big difference between Lubavitch, Bobov, Satmar, and Breslov, in Chassidish. There are very clear differences.
Now by Yeshivish, you have the shtark Yeshivish Lakewood chevrah, but you also have chevrah like Chofetz chaim guys who aren’t so yeshivish but they aren’t modern either. Same for yeshivos like Chaim Berlin or Torah Vodaas…
Even in MO there’s differences which I am less familiar with so I won’t comment on.