Yes, everyone sees the same phases of the Moon. People north and south of the equator do see the Moon’s current phase from different angles, though. If you traveled to the other hemisphere, the Moon would be in the same phase as it is at home, but it would appear upside down compared to what you're used to! For example, on March 8, 2021, the Moon was in a waning crescent phase. Seen from the Northern Hemisphere, the waning crescent appeared on the left side of the Moon. Seen from the Southern Hemisphere, the crescent appeared on the right.