full moon; moon on the 15th day of the lunar month
Refers to the full moon, especially in the context of the lunar calendar where the 15th day is the night of the full moon.
Tonight is a full moon, and the sky is bright.
full moon of the eighth lunar month
Only with reading もちづき
Specifically the full moon of the eighth month in the lunar calendar, associated with the mid-autumn harvest moon festival (十五夜). Restricted to the reading もちづき.
The full moon of the eighth lunar month is celebrated as the harvest moon.
A beautiful full moon is out tonight.
I drank sake on the porch while gazing at the full moon.