Frequency and Cause
One of the fundamental differences between a new moon and a lunar eclipse is the frequency in which they occur. A new moon happens once a month and a lunar eclipse approximately two times a year. Since the moon itself doesn't project any light and simply reflects that of the sun, a new moon occurs when the earth is positioned in such a way that it blocks the sun from illuminating the moon. A lunar eclipse requires a full moon to be present. The eclipse occurs when the moon passes behind the earth and the earth blocks the sun's rays from striking the moon.
Position
During a new moon, the moon is positioned between the sun and the earth. During a lunar eclipse, the earth is positioned between the sun and the moon. Throughout the progress of a lunar eclipse, the earth gradually moves into a position that, at first, blocks only part of the moon. This is called a partial lunar eclipse. Later, the earth moves into a position where the entire moon is blocked out, with light only being emitted from the moon's periphery.
Visibility
Another difference between a new moon and a lunar eclipse is the visibility of each phenomenon. When a new moon occurs, no sunlight is reflected off the moon and the moon cannot be seen. Only the back of the moon is illuminated during this phase. In the case of a lunar eclipse, as the earth moves into position, most of the sun's reflected light is blocked, but you can see light radiating around the moon's periphery.
Duration
The length of time each phenomenon is observable also varies. When a lunar eclipse occurs, its duration is usually between one and two hours. Whenever a new moon occurs, the moon is not visible for the duration of an entire night.