How did the grains of sand from the moon differ from the grains of sand from the earth?

If you are talking about typical sand you would find at the beach or in a river bed here on Earth, there are some differences. I would say the first biggest difference is in composition and mineral make up. Although the Moon is largely made of the same materials as Earth’s mantle and surface, the Moon experiences very little weathering (no liquid water and virtually no atmosphere). "Earth" sand is typically composed mostly of quartz grains. This is because quartz is highly resistant to both physical and chemical weathering. Most of the other minerals originally with the quartz are broken down into fine clay and carried away, chemically eroded / dissolved, or some combination of the two. This usually leaves only the quartz behind, and so most of the time when you see/think of sand, you are talking about quartz. Without these weathering mechanisms on the Moon, the "sand" (which is likely more silt or clay sized grains anyways) would consist of mostly other minerals like anorthosite, olivine, and proxene.