Solar Eclipses happen when the moon shifts ahead of the sun. During a solar eclipse, it gets darker and darker as more of the sun is covered by the moon. When the moon is in it's umbra and entirely covered, it is called a total solar eclipse. When the moon is in it's penumbra, it is called a partial solar eclipse. A total eclipse is the only time we can see the sun's corona, which is the ring of light we see around sun during the eclipse. It can also only occur during the day and during the new moon.
Lunar eclipses occur when the moon passes directly behind the earth causing the earth's shadow to cover the moon. When it's in the umbra, it's called a total lunar eclipse and is entirely covered. When it's in the penumbra, it's a partial lunar eclipse. They only happen during a full moon and at night.