At my alma mater, Latin honors have hard GPA cutoffs. Summa cum laude is a 3.8 or higher; magna cum lauda is a 3.6 or higher and cum laude is a 3.4 or higher. My college doesn’t practice grade inflation so the percentage of students who get Latin honors is smaller than 50%, although I’m not exactly sure what it is.
Other requirements were for departmental honors, not Latin honors at my alma mater. You could get departmental honors if you took the honors seminar and wrote a senior honors thesis, but that wouldn’t affect whether or not you got Latin honors.