1. Partial Solar Eclipse: This happens when the Moon passes between the Sun and Earth, but the alignment isn't perfect. The Moon doesn't completely cover the Sun, leaving a portion of the Sun visible. The amount of the Sun covered varies depending on the location of the observer.

2. Partial Lunar Eclipse: This occurs when the Earth passes between the Sun and the Moon, casting a shadow on the Moon. However, the Earth's shadow doesn't completely cover the Moon. This results in only a portion of the Moon being eclipsed.

Both types of partial eclipses can be fascinating events to witness, although it's always crucial to take proper safety precautions when observing a solar eclipse.