An eclipse happens when a celestial body enters the shadow of another, blocking the Sun's light. The essential difference between a lunar and a solar eclipse lies in who aligns in the middle and where the shadow falls: in a lunar eclipse, the Earth projects its shadow onto the Moon; in a solar eclipse, the Moon projects its shadow onto the Earth.
In terms of alignment, a solar eclipse occurs with the order Sun – Moon – Earth, where the Moon totally or partially blocks the Sun as seen from Earth. A lunar eclipse follows the order Sun – Earth – Moon, with the Earth's shadow covering the Moon. A solar eclipse is only possible during a New Moon, while a lunar eclipse only happens during a Full Moon.
Safe observation is a crucial difference. Lunar eclipses can be viewed with the naked eye without special protection, as you are looking at the Moon. However, directly observing a solar eclipse, even a partial one, requires adequate eye protection to prevent permanent retinal damage.