Height Safety is a more general industry term for safe practices of work when above the ground. Whereas fall protection and fall arrest are more narrow fields, working at height includes safety ladders, ladder safety, platforms, roof safety, height safety systems, safety gates, scaffolds and scaffolding, edge protection, mobile access equipment, towers, mats, etc.
Risk assessments for height safety
As you can see the list is quite long. Proper risk assessments should be carried out to ascertain the safest way for you to go about that particular task. The job has to remain possible but should never be carried out if dangerous. Height safety gear might include fall protection equipment or fall arrest but these are only a small part of this large subject.