Daniel, living in the time of Babylon, sees the beasts rise out of the water in a specific order. From them stemmed the Little Horn Entity.
John, living in the time of Rome, sees the beast as a mix of the ones of Daniel but lists them in backwards order. This is the culmination as a mix of this entity as it held to many elements of the 4 nations it came out of.
(Babylon, Persia, Greece, Rome)
Daniel was looking forward in time....
John was looking backward in time....
BOTH were seeing the same entity.
Daniel saw.....
And four great beasts came up from the sea, diverse one from another.
The first was like a lion, and had eagle's wings: I beheld till the wings thereof were 
plucked, and it was lifted up from the earth, and made stand upon the feet as a man, and a man's heart was given to it.
And behold another beast, a second, like to a bear, and it raised up itself on one side, and it had three ribs in the mouth of it between the teeth of it: and they said thus unto it, Arise, devour much flesh.
After this I beheld, and lo another, like a leopard, which had upon the back of it four wings of a fowl; the beast had also four heads; and dominion was given to it.
After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns.
Daniel 7:3- 7
John saw.....
seven heads and ten horns, and upon his horns ten crowns, and upon his heads the name of blasphemy.
And the beast which I saw was like unto a leopard, and his feet were as the feet of a bear, and his mouth as the mouth of a lion: and the dragon gave him his power, and his seat, and great authority.
Revelation 13:1,2