If there is fire safety are there more types of safety?

Yes, there are "types of safety" for just about anything dangerous that people perform while at jobs or while on public ways or in places open to the public.

For instance, there are: highway safety for the roads and passenger safety in airplanes; "occupational safety" or industrial safety (OSHA and similar rules elsewhere); scientific laboratory safety; school safety; construction safety; public safety (police, lifeguards, firefighters, EMS, etc); etc.