This exactly.
Back to the OP's comment. Why we refer to the white wire as the identified grounded conductor. Bonds are called the grounding conductor. Hots are called the ungrounded conductors. Trying to change 100 years of describing something is going to take time though.
I have never heard that specific terminology, but it seems about right for the standard wiring in North America.
for 3 phase systems, you have the choice of Y or delta wiring. Both could be with or without a ground, but only the Y layout has a neutral. The delta arrangement is almost always used for long distance transmission, and the Y arrangement is typical for short distances (within a single building or floor)
for single phase, you have the choice of hot - hot (phase to phase) or hot neutral. For standard residential, hot - hot will be either 240v or 208v nominal (depending on the transformers on the street - they could be split tap or 3 phase) and hot - neutral is 120v nominal.
In all of these cases, neutral means that the wire will carry current, but is not energized from a power source. It goes to a grounding rod or some other sink that the energized wire(s) push electrons into, and pull them back out of as the voltage alternates. In a single phase hot-neutral system, the current in both is balanced except in the case of a fault. Ground fault breakers work by checking that the current in each is balanced for example
For all of these designs, the addition of a dedicated ground wire is designed to provide an alternate path for electrons from the energized conductor to a ground sink in case something fails. These wires do not normally carry any current, and it is expected that all of the housings (electrical boxes etc.) will be connected together to provide a level of redundancy in the path to earth. Isolated ground systems are different.
Grounding provides an added level of safety principally in the case of mistakes. Mis wired equipment, loose conductors, voltage spikes and anything else that can generate an arc. Worn insulation or bad environmental conditions too. The grounding wires themselves don't intrinsically add more safety, but the idea is to add more redundancy in the safety failback path because people make mistakes