A Lunar Eclipse refers to the Moon falling within the shadow of the Earth when the Earth is directly between the Sun and Moon. This alignment coincides with a Full Moon.
A Solar Eclipse happens when the Moon comes between the Earth and Sun and the Moon castes it shadow on a small area of the Earth. This alignment takes place only in conjunction with a New Moon when the Illuminated side of the Moon is turned completely away from the Earth.
Because the Earth is much larger than the Moon, the Earth's shadow can completely cover the Moon during a Lunar Eclipse, so that only the Sun's light refracted by the Earth's atmosphere illuminates the Moon, whereas, with a Solar Eclipse the Moon can only project a small shadow on the Earth under ideal circumstances.
Not all Full or New Moons produce an eclipse since the Earth and Moon usually pass above or below the others shadow.