It's the Juubi's corpse. Blaze Release is right, when Nagato used the corpse, he animated it with his chakra. But, more than that, the will of Gedo against Hanzo's forces was all Nagato. He was puppeteering Gedo like Sasori would puppeteer any corpse he acquired. Like BR said, what's going on with Tobi is different, in that he is putting the tailed beasts inside of Gedo, giving Juubi some semblance of life again, sort of like a giant edo. I think he, theoretically, could have put Kisame's consciousness and chakra into Gedo, and it would have been much the same situation as we have now with Shukaku in Gedo. But he's not trying to just bring Gedo to life, he's trying to bring back the Juubi, and that requires chakra from all nine tailed beasts, which he arguably has, though he's a bit short on 8 and 9, fused together. When he has just Shukaku in Gedo, I think he just needs to control Shukaku, but, with 7 of the 9 in there, he needs to control all seven simultaneously. It's not one mind in there yet, except when it is just Shukaku, and he will have to do something to fuse them all back together.