Only 19 Gear Set Slots for 23 Jobs/Classes

[Niwashi]

But where did i get the other 8 slots in my case and 9 slots in LunaChilds case?

You start with several. When gear sets are first unlocked (one of the first few class quests, either level 5 or 10, can't remember) you get immediate access to making multiple gear sets even though you'll only have one class so far at that point. That would be where your extra 8 came from, the initial bunch you get when the feature is unlocked. Then you get one more each time you unlock another class or job.

I don't know, however, why it doesn't seem to be consistent. Why LunaChild, for instance, has one more than you do even though both of you have all classes and jobs unlocked. He must have done something else that also unlocked an extra get set slot. (Could it be a legacy thing, maybe? From what I understand, FFXIV 1.0 didn't require "unlocking" of different classes the way ARR does, so their initial gear sets would have been handled somewhat differently.)