What exactly is the relationship between the magic classes?

[Enkidoh]

You have to remember though, when 1.0 was first released, classes were a lot different in how they functioned to how they are now (for instance, CNJ originally had the use of spells of all elements, including Fire, Lightning and Ice), and Jobs were not even in the game at all - they were only added towards the end of 1.0's life, hence classes had to be completely overhauled to compensate.

This is why THM lost Sacrifice, as it's traditionally a White Mage ability, and THM was made to upgrade to Black Mage, gaining the CNJ's Fire, Ice and Lightning spells (because CNJ was made to upgrade to WHM and focus more on healing). It had nothing to do with the lore of the class - it was purely to balance gameplay mechanics.