Lunar Phase / Phases of the Moon
The apparent form of the Moon changes every day as it moves around the Earth. This is called lunar phase or phases of the Moon.
Times of New Moon, 1st Quarter, Full Moon and Last Quarter are those when Δ λ = longitude of the Moon - longitude of the Sun becomes 0°, 90°, 180°, 270°, respectively.
Lunar Age / Age of the Moon
Lunar age or age of the Moon is the amount of time elapsed since New Moon measured in days.