Thomas, Alito, Coney Barrett tend to be partisan conservatives.
Kavanaugh, Gorsuch, Roberts, and Kagan tend to be mainstream jurists (whether that's "institutionalist," I'm not sure). If you see Kagan side with the conservatives or Gorsuch, Roberts, or Kavanaugh side with the liberals, it's usually in favor of the mainstream, centrist, legal establishment view. The differences between them tend to relate to mainstream legal debates (e.g., the proper role of Chevron deference in the administrative state; Kagan was an admin law professor, whereas Gorsuch in particular is skeptical of Chevron deference).
Sotomayor, Brown Jackson tend to be partisan leftists.
Thomas, Alito, Coney Barrett tend to be partisan conservatives.
Kavanaugh, Gorsuch, Roberts, and Kagan tend to be mainstream jurists (whether that's "institutionalist," I'm not sure). If you see Kagan side with the conservatives or Gorsuch, Roberts, or Kavanaugh side with the liberals, it's usually in favor of the mainstream, centrist, legal establishment view. The differences between them tend to relate to mainstream legal debates (e.g., the proper role of Chevron deference in the administrative state; Kagan was an admin law professor, whereas Gorsuch in particular is skeptical of Chevron deference).
Sotomayor, Brown Jackson tend to be partisan leftists.