Short answer: No, neither of those is correct.
Long and poorly thought out answer: A typical full moon occurs once a month. When the moon is full, it is in a position that places the Earth between itself and the sun. The Earth is not directly between the Moon and Sun during a full moon obviously, because that would cause the Earth Eclipse of the Sun that we see in the video. But instead, it's orbit is offset by a given amount so that light travels past the Earth.
Kinda hard to explain without a diagram, but if you could follow that then you'd see why the Earth's Eclipse of the Moon is not extremely common.