Smaller versions or regular required courses offering greater depth and more discussion
Nearly any course at UF could have a Honors version. For example, Physics I Honors covers Newtonian physics (like regular Phyiscs) but adds material on special relativity. Because the students are in Honors, the basic material can be covered a bit faster leaving room for some more advanced concepts. Unfortunately, the Honors program does not have resources to support these offerings. So they typically occur when a department has to offer a lot of sections of course, and can therefore allocate one section of the many to Honors students.
When offering an Honors section, we do not want to students to suffer a GPA penalty for taking it. Students should be held to the same level of mastery as a regular section. If they have mastered the material at an "A" level for the regular section, they should get an A for the Honors section. The extra material and discussion will help prepare them better for subsequent classes and expose them to more difficult concepts.