So yea, Madara was revived as an edo tensei, but when it was undone, he released himself from the Edo tensei contract, thus removing the label "Edo" off of himself.
Now, he is an immortal being, who can never tire or die.
He isnt dead, or else he'd be gone. He is no longer bound to this world be some kind of, Madara is bound to this world as a living soul in a body.

So now we should refer to Madara as...well, Madara, with some Senju DNA of course.
Just like Obito has Senju DNA..except he isnt immortal.
Just like Danzo and Yamato got Senju DNA..except not at such a high level.

He is no longer Edo Madara.