The Red Giant has seen a variety of names in its appearances. Its Japanese name is "Wolframiter": "Wolframite" with the "er" word-ending. In its original appearance in Final Fantasy VII the name was erroneously localized as "Wolfmeister" (would would be written ウルフマイスター (Urufumaisutā?) in Japanese).
In its other appearances no attempt has been made to keep the original Japanese meaning. Its common name "Red Giant" originating in Final Fantasy VIII refers to its status as a red version of the Iron Giant.
Its third name in three appearances, "Red Giant" wouldn't apply in Final Fantasy X where the enemy appeared as a pair of red and blue enemies, so they were named Gemini referencing that they were a pair. In Final Fantasy X-2 only one of the pair returns losing this context.
The Armored Fiend is not an official Red Giant appearance. Known in Japanese as "Demon Soldier" (まじんへい, Majin-hei?), it is a red palette-swap of the Armor Construct, whose Japanese name is "Giant Soldier" (きょじんへい, Kyojin-hei?). When Armored Fiend was named "RedGiant" in its original appearance on SNES, the Giant Soldier enemies had no relation to the series's Iron Giants. However the Advance release introduced the standard Iron Giant as a blue Giant Soldier, thus retroactively making the Armored Fiend a true red Iron Giant.
Red Giant appears as an optional boss in Ultimecia Castle. It is summoned when the player retrieves the Prison Key from the Prison Cell in the Armory. It gives verbal responses that are triggered when the player uses certain actions against it. Red Giant fights with a sword until it's HP drops below 9000, at which point it drops the sword and fights with fists instead.
Two versions of the Gemini are fought together in the final dungeon, one blue giant wielding a sword and one red giant wielding a club. When together, they can attack using the skill Double Reaper, while alone they fight using Reaper and Leaping Swing.
Only the red Gemini returns as an enemy fought at Besaid, Thunder Plains, Mt. Gagazet, and Via Infinito floors 21-23. It fights using the physical attacks Skullcracker and Reaper, and when in Oversoul, will instead use a wide arrange of -aga elemental magic in addition to White Mage-Hater.
Wolframite is a tungsten-based mineral containing iron, and is a primary source of tungsten ore.