It's like the Bard situation, where there is the minstrel type who are travelling musicians earning coin by singing in taverns and the like... and the actual Discipline of War (Job class) that are Archers who started singing songs in battle to inspire their comrades - two seperate concepts which also are similar.

The confusion with the WAR Job and the Warrior of Light term goes back to the original FFI where the concepts first originated, (FFXIV owes a lot to the original FF game), and the two ideas from then on became reoccurring elements throughout the FF series, WAR as a reoccurring Job, usually a physical damage dealer that specializes in most weapon types but tended to favour axes or swords, and the Warriors of Light which was usually the term given to the player characters in the earlier FF games (the term kind of dropped out of favour by FFVI, only to be 'rediscovered' later on when Square started rereleasing touched up versions of the early FF games on modern consoles), and it's use here in FFXIV is part of Yoshi's desire to have FFXIV honour and reference the FF series in general.

Interestingly there was little confusion in the original NES version of FFI between these terms as they were translated slightly differently - the WAR Job was actually known as Fighter in the original NES FFI, and the 'Warriors of Light' were written actually as the 'Light Warriors', so the confusion is more a modern thing, ironically.