Are the song of Moses and the song of the Lamb the same song or two different songs?
They are two separate songs. The tribulation saints in heaven sing both the song of Moses, the servant of God, and the song of the Lamb. The song of Moses looks back to Exodus 15, when Israel came through the Red Sea, while the song of the Lamb is distinct.
Les explains that in Revelation 15, the martyred tribulation saints who had gotten victory over the beast, his image, his mark, and the number of his name are standing on the sea of glass mingled with fire, having the harps of God. They sing the song of Moses, the servant of God, and the song of the Lamb, and Les emphasizes that those are two separate songs. The song of Moses is tied to Exodus 15, where Israel had just come through the Red Sea and were gathered around Mount Sinai, perhaps not even quite to Sinai yet. So the two songs are distinct: one recalls Israel's deliverance at the Red Sea, while the other is specifically the song of the Lamb.
And they sing the song of Moses the servant of God, and the song of the Lamb, saying, Great and marvellous are thy works, Lord God Almighty; just and true are thy ways, thou King of saints.