Looks like it was Zelda who said it, not the Red maiden, but:
"Ganon... this beast was once
of the Gerudo... Once human.
He was called Ganondorf!
King of Darkness, ancient
demon reborn. The wielder
of the trident!!"
(bold emphasis added)
The King of Darkness is evidently an "ancient evil", which is to say, an evil from the past. That he is reborn furthers this idea that they are referring to the Ganondorf seen in Ocarina.
HOWEVER. Given that this Ganondorf has a radically different backstory - where the Gerudo claim he was a criminal for the majority of his life and was eventually exiled for entering the pyramid (compare to the Ocarina version of Ganondorf who was still revered among the Gerudo (they still call him the great Ganondorf in the adult time period) when he rose to power) - it stands to reason that this is a NEW Ganondorf, be it a reincarnation of the previous Ganondorf or a new individual all together, but either way, a new body, a new threat - not the same Ganondorf as in Ocarina of Time.