Lots of confusion generated by the marketing and some YouTube videos, so here's a very simple summary for the FAA's rules:
Flying for recreation (exemption under 107): Exempt from registration but all other rules apply, including proximity and controlled airspace
Flying under part 107: No exemptions at all. Registration required and all other rules apply.

Flying for recreation (exemption under 107): Exempt from registration but all other rules apply, including proximity and controlled airspace
Flying under part 107: No exemptions at all. Registration required and all other rules apply.
