The differing lines are these:

Quote Originally Posted by Y'mhitra for 1.0 character
You were there at the Battle of Carteneau. You were there on the day of the Calamity when aether infused with the dragon's essence rained down upon the field.
Quote Originally Posted by Y'mhitra for 2.0 character
On the day of the Calamity, the dragon vanished in an explosion so massive that his aether was carried to the far corners of Eorzea. You, among many others, have already been touched by his essence.
The fact that the PC can cast Teraflare is also linked in the lore book to this same concept:

Quote Originally Posted by Lore Book on Teraflare
All those who bathed in the dreadwyrm's scattered aether during the Seventh Umbral Calamity posses the latent potential to master this mighty summoner spell.
So it looks like they're pretty much all ways of saying the same thing, its just that the affected area is bigger. Which is good for those of us over in Othard during the initial Teraflare cast for RP reasons? :P

Or... the Allagans came up with techniques the required the user to survive a primal ult before being able to actually do the technique. And these would be the primals that have too much aether for us to make egi's out of which also require the user to survive killing a primal... *thinks about what it would be like to be facing down the entire Warring Triad and Bahamut at once with no DWT or egi*