An annular eclipse is seen from earth when the moon comes between the earth and sun, but the lunar disc is a trifle too small to completely cover the sun, even though it moves directly across the sun.
An eclipse of the moon, as we see it from earth, is quite different. During a lunar eclipse, the moon does not get between earth and sun. It moves into the shadow of the earth. The earth's shadow is so huge compared to the moon that we can never have the situation where the earth's shadow scores a direct hit, but a ring of moon remains uncovered.
Likewise, moon people could never see an annular eclipse of the sun. An observer on the moon, during what earthlings see as a lunar eclipse, would see a total eclipse of the sun, in which the huge earth completely blocks the sun's face for hours, or a partial eclipse in which the earth scores a near-miss. It cannot happen from the moon, however, that the earth appears smaller than the sun's disc. The earth is just too big.