I dont believe the children are actually specified. All that we know is the war shattered the world, kingdom hearts was lost and the Xblade somehow destroyed.
In the wake of this the world reforms as one of several realms and countless worlds within those realms. The keyblade made to imitate the Xblade is then repurposed as a weapon of balance to keep the new world order intact so the same tragedy isn't repeated.
The origin of the 7 PoH or why theres even seven to begin with is a mystery and unexplored territory. Even the full extent of their roles and powers aren't known. So far we only know they act as the lock and key to the Door to Darkness from KH1.
Indeed, who exactly those children were, even how many there were, is not specified at all.
Yen Sid talks about it in DDD:
Yen Sid said:
The Keyblade Wars of yore plunged the true Kingdom Hearts into darkness, and the Chi-blade was shattered.
But the light still shining in the hearts of children rebuilt the world that we know today.
Notice how Yen Sid specifies that "the light shining in the hearts of children" has nothing to do with the light parts of the shattered X-blade.
As for the seven hearts of pure light (The Princesses), we do get more information on them, including a confirmation on the often misinterpreted fact of the correlation with the seven light shards of the X-blade.
Unlike some fans claim, the seven light shards of the X-blade
are NOT the seven pure hearts of the Princesses:
DDD said:
Yen Sid: And the light from the broken Chi-blade was then divided into seven, to protect the number of pure hearts in the world.
Mickey: Seven pure lights. They're...the princesses of heart.
Yen Sid: Indeed. Those seven pure hearts form the very source of all light in the world. If they are lost, the world will again give way to shadow.
Thus, even if we deliberately avoid finding our seven lights to avert another Keyblade War, Xehanort will still target the seven princesses in order to forge the Chi-blade.
In the first statement, Yen Sid explicitly states that the light part from the X-blade was divided in order
to protect the number of pure hearts (the Princesses).
This plainly shows that the seven light shards (the protectors) of the X-blade are
not identical with the seven pure lights.
What Yen Sid however also warns about is that the seven pure lights that are the Princesses can be used as a substitute to also fill out the formula for forging the X-blade, as the glossary tells us that:
DDD glossary said:
The letter χ can be pronounced both "key" and "kye" (leading to some confusion) and symbolizes the perfect crossing of light and darkness. The χ-blade can be forged via a high-dimensional clash between those two poles.
This tells us that the actual main
condition for forging an X-blade is just to have a high-dimensional clash between equal powers of light and darkness. This is also why the clash between Ventus and Vanitas actually produced an X-blade and why Xehanort even tried out/experimented with this "shortcut".
What Xehanort didn't count on and what apparently makes a difference is that in order to reach the mentioned
perfect crossing of light and darkness you need to follow a specific formula that was off with Ven and Vanitas. You can theorhetically produce an X-blade with any clash of equal darkness and light poles, but the strongest, most refined variant can only be created in one way.
Back to the Princesses though, Yen Sid's statement about "
Those seven pure hearts form the very source of all light in the world" teaches us that the seven Princesses are indeed the replacement/substitute for the original/true Kingdom Hearts which was lost to the darkness after the first Keyblade War, since this original/true KH was
also stated to be the source of all light in the old world:
Yen Sid said:
And as for the source of all light--the one true Kingdom Hearts--it was swallowed by the darkness, never to be seen again.
This can even be connected to the prophecy:
"on that land shall darkness prevail and light expire" is
exactly what happened at the end of the great Keyblade war which caused the end of the old world. Darkness
did prevail and flooded the Realm of Light, and the Light (in the form of the true KH) expired and was swallowed by the darkness.
Now, in the current world, if all seven Princesses fall, history will repeat itself as Yen Sid states: "Those seven pure hearts form the very source of all light in the world.
If they are lost, the world will again give way to shadow."
In that bold part above, Yen Sid practically quotes "on that land shall darkness prevail and light expire" in his own words.
This is the great danger that hangs over everything and this is also why Yen Sid may think he can throw a wrench into the prophecy by training Kairi, one of the pure seven. Unlike in the first world, where there was only
one source of all light, the current world as
seven and as long as at least one of those still stands, the prophecy may be prevented from repeating.
By training Kairi, the light thus may actually endure long enough this time to allow for a different outcome than the original war had. With this bought additonal time though it would probably fall to Sora (and any allies that are still left) to find a proper solution before Kairi's strength finally wanes as well.