The partialsolareclipse occurs when the Moon only covers some of the Sun's disk, and casts it's penumbra on Earth.
The annular solar eclipse occurs when the Moon is near the Apogee, the furthest point orbit of the Moon from the Earth, and casts it's antumbra on Earth, leaving the outer edges of the Sun's disk visible.
The penumbra is the larger but fainter shadow that both the Earth and the Moon can cast onto each other.
The umbra is the smaller but much more intense shadow that both the Earth and Moon can cast onto each other.
The antumbra is the extension of both the Earth and Moon's shadow. Only the Moon's antumbra can be casted on Earth, because the Moon's orbit cannot reach the Earth's antumbra.
The total solar eclipse occurs when the Moon is near the Perigee, the point of the Moon's orbit closest to Earth. This causes the Moon to entirely cover and obscure the Sun.
The hybridsolareclipse (Annular-Total eclipse), is the rarest type of solar eclipse. They occur when the eclipse transitions from an Annular eclipse to a total eclipse, or vice-versa.
The penumbral lunar eclipse occurs when the Moon is passing through the Earth's penumbra. This lunar eclipse is hard to observe, and is barely noticeable.
The partial lunar eclipse occurs when a part of the Moon is passing through the Earth's umbra. This eclipse can last as long as 3 hours and 40 minutes.
The total lunar eclipse occurs when the Moon is entirely covered by the Earth's umbra. This eclipse can last as long as 1.5 hours.