The moon as seen from the surface of the Earth is lit directly by the sun, unless it is during a new moon. It's very easy to meter the moon with a sufficiently narrow enough light meter. Even built-in camera meters can do it if the lens magnifies the moon sufficiently to occupy the full area of a camera's spot meter. Just remember that an uncompensated reflective meter reading will assume you want the metered area to be halfway between white and black. If you want the moon to appear bright, you'll need to compensate by exposing a stop or two brighter.
Or for photographing the moon itself you could just use the "lunar 11" rule-of-thumb that is similar to the "sunny 16" rule-of-thumb when the moon (or sun) is about 20° or more above the horizon. "Lunar 11" says to use a shutter time that is the reciprocal of your ISO with f/11. As usual, atmospheric conditions can affect how much of the sun and moon's light reaches the surface. The "lunar 11" rule-of-thumb assumes a clear, cloud free sky, just like the "sunny 16" does.
The night time landscape under a moon is not directly lit by sunlight. How bright it will be will depend upon how much of the moon's disc is illuminated as viewed from the location in question. It will depend upon how much of the moon's light is absorbed by clouds, water vapor, and other particulates in the atmosphere. It will depend on how high the moon is above the horizon.
Under a very bright full moon high in the sky on a clear, relatively dry, and cloudless night a moon-lit landscape will typically meter at around EV -2 to EV -3, depending on the reflectivity of the landscape. A desert with white sand or a snow covered plain might meter at EV -1 under perfect lunar conditions.
EV -2 to EV -3 is beyond the capability of the internal light meters of even the top professional camera models today. Although some can autofocus down to EV -2 or EV -3, their light meters are rated only to EV 0 or brighter.
There are a few high end electronic handheld light meters that can measure down to EV -5, but somewhere between EV -2 and EV 0 is much more common. Older analog handheld light meters were even more limited. The popular Sekonic L-208 had a range of EV 3 to EV 17. The Sekonic L-398A Studio Deluxe III had a range of EV 4 to EV 17 for incident metering and only EV 9 to EV 17 for reflective metering. EV 3 is five stops, or 64 times brighter than EV -2.
When the moon is not full, or lower in the sky, or partially or fully obscured by clouds, or diffused by high humidity or dust and other particulates, or any combination of these factors, the landscapes it illuminates are very quickly too dark to be effectively metered by the vast majority of available light meters. Even the top end meters, such as the $600 Sekonic Speedmaster L-858D-U, can't keep up for very long as a night landscape can be significantly darker than EV -5.