Many folks write or read the terms Haredi, ultra-Orthodox, Hasidic/Hasid, and yeshivish without knowing what those words mean.

This might help a bit.
Caveat:

Jews are people, too. Individuals or communities who/that identify in one of these subgroups may not have perfect alignment with these bullet points, particularly when it relates to their personal approach to text / understanding of theology. When in doubt, ask.
Chabad and Satmar, two groups you may have heard in the news recently?

Those are two (out of literally hundreds of) Hasidic sects — and yes, they have very different practices, dress, hats, cultures, views towards Israel, standards for women, and on and on and on.
When I use rationalism + mysticism above, I'm not describing individual approaches but rather a very particular tension in modern orthodoxy (NOT to be confused w/ Modern Orthodoxy, though there too). This course description I found online (thanks, U of Haifa) summarizes it well:
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