In bicycle hydraulic brakes, there are systems designed for DOT (3/4/5.1) brake fluid, and systems designed for mineral oil. Using the wrong fluid can damage seals and cause terminal failure (and death).
As far as I know, all oil used in MTB suspension is essentially the same basic fluid, plus additives. Citroën did use mineral-based "LHM" fluid for decades but eventually gave in and fell in-line with the rest of the auto industry.
Bicycle suspension forks tend to use light oils.
Gear oil will be too thick. Motor oil may have additives to help it perform in an engine which might interfere with the operation of your fork. The first three in your list are usualy synonyms.
The owner's manual for your fork should specify the oil grade and either a volume to measure or a method to judge the right level. If your fork also uses grease, I'd be more concerned about using the original manufacturer's fluids and grease, but otherwise any suspension oil of the correct grade should be fine.