It can be surprising that many people believe that the lunar phase is caused by the Earth casting its shadow on the surface of the Moon. Flat-Earthers are no exception. But they take it one step further and use the misconception do “disprove” the fact that Earth is a sphere. They are wrong. The lunar phase is the shape of the sunlit part of the Moon seen from the observer.
On the other hand, the phenomenon where the Earth casting its shadow on the surface of the Moon is called the lunar eclipse. Moon phase occurs all the time and undergoes a monthly cycle, while a lunar eclipse happens only a couple times in a year.