Illumination and viewing angle
Half of the Moon is lit by the Sun at a time. As its position around Earth changes, we see different fractions of that lit hemisphere. A crescent does not mean Earth’s shadow covers most of the Moon.
Why every full Moon is not eclipsed
The lunar orbit is inclined to Earth’s orbital plane. Most full Moons pass north or south of the shadow. Eclipses occur when the alignment is near an orbital node; a solar eclipse uses the corresponding new-Moon alignment with the Moon between Earth and Sun.
Compare lunar and solar visibility
A lunar eclipse can be viewed from the night side where the Moon is above the horizon. The Moon’s solar-eclipse shadow crosses a much narrower region. The moving shadow and contact times require positions and distances, not only a drawing of three circles.