Difference between core curriculums and distribution requirements?

My thought is that core curriculums are specific courses required for graduation, whereas distribution requirements give you range of subjects to choose from. Is this right? This really confuses me…
Also, I see that brown is famous for having no core or distribution requirements. What are some other top colleges that have open curriculum policy?

“Is this right?”

Yes.

Some colleges with open or flexible curricula:

Smith, Hamilton, Grinnell, Amherst. The University of Rochester requires six courses, distributed three and three, in major fields outside of the student’s primary concentration.

The core curriculum at Chicago or Columbia is more than just a few specific courses.
At Chicago it is an integrated set of (mostly) year-long course sequences spanning the humanities, social sciences, biological and physical sciences. These courses can take up much of your first two years. Many of them are developed and taught by teams of instructors appointed to “the College” at large (not to specific departments). Most core classes are small (< 20 students); they often emphasize group discussion of primary source materials. They are not survey courses taught in large lectures with accompanying text books. There typically is a choice of several courses offered to satisfy each of the major core requirements.
https://collegeadmissions.uchicago.edu/academics/core

A set of distribution requirements at other colleges may or may not resemble an integrated, common core. It may be more like an old-fashioned “Chinese menu” (“one from column A, one from column B” chosen freely by the customer) rather than a prix fixe, table d’hôte meal of in-season items selected by the chef to complement each other.