"What exactly is "full hydraulic steering?"
The expression refers to any of various steering system configurations where a vehicle is steered solely by means of a hydraulic circuit comprising, as a minimum, a pump, lines, fluid, valve, and cylinder (actuator). that is to say, the vehicle is steered (usually via the front wheels) purely by a hydraulically powered steering cylinder. This is an important distinction from "hydraulically assisted" steering, where hydraulic power serves only to assist a mechanical steering system (as is the case with the every-day Saginaw hydraulically assisted power steering on virtually every light car / truck on the road today), and is also the reason for the inclusion of the word "full" (as in FULL Hydraulic steering) in common use. It indicates that the vehicle is steered ONLY by hydraulics, with no other system (mechanical linkage) in place.
Hydraulic steering has been used forever on a huge number and variety of pieces of equipment - from small forklifts and garden tractors to combine harvesters, large tractors, massive earth moving equipment, construction and mining equipment, aircraft, boats, ships, and many many others.
The correct industry term for this kind of "full" hydraulic steering is HYDROSTATIC STEERING.