The short answer
What is the difference between a roofer and a handyman?
A roofer holds a Florida contractor license for roofing. A handyman usually does not, and can only do small, casual jobs without one.
Chapter 489 of the Florida Statutes licenses contractors by trade. Section 489.105(3)(e) defines a roofing contractor as one whose services are unlimited in the roofing trade, with the experience, knowledge and skill to install, maintain, repair, alter, extend or design roofs. It covers roofing, waterproofing and coating (with one exception for coatings not sold as leak or life-extending fixes). The scope also includes required roof-deck attachments and repair or replacement of wood roof sheathing or fascia during a roof repair or replacement.
A "handyman" is not a license in that chapter. The Florida Department of Business and Professional Regulation (DBPR) uses the word only for small jobs that are exempt: its FAQ says handyman jobs where total construction costs are below $2,500 are exempt from state licensure. Everything else about that exemption is narrow, as the next sections show.
A roofing license also comes in two kinds. DBPR says a certified contractor holds a certificate of competency from the state and can work in any jurisdiction in Florida. A registered contractor is registered locally and can work only where the registration was issued. Coastline's owner, Josh Hildebrand, holds a state certified roofing contractor license, CCC1331076, that DBPR lists as current and active.