The answer is a classic yes and no. In general, the moon has an earth-bound orbit, which means we always see the same side. Always and everywhere. While the earth rotates once in 24 hours, the moon moves about 1/30 on its axis. This hardly changes the angle between the sun, moon and earth. So the phases of the moon are the same in the world. When there is a full moon there is a full moon everywhere.
Do you always see the same side of the moon from all over the world?
Depending on the angle, the moon can appear differently in different places. However, that is not the only difference. Depending on the point on earth you look at the moon, you have a different perspective. This is because the earth is round.
The visible surface of the moon can, depending on where it is observed on Earth, actually vary a little. However, this does not mean that you can somehow see the entire back of the moon from the ground.
Overall, 59 percent of the lunar surface can be observed from the earth (due to various effects). The rest cannot be seen – no matter where we are on Earth.
You can imagine the movement of earth and moon as follows:
You sit in a carousel (earth) that rotates quickly and a man (moon) slowly walks around the carousel in the direction of rotation.
Someone who sits in the carousel on the opposite side, of course, always sees this man in a slightly different place than you.
And by definition, a full moon is the moment when the moon is in the opposite direction from the center of the earth to the sun. So the full moon takes place all over the world at the same moment.
It can roughly be said that the phase in which the moon appears fully illuminated to an observer on earth takes about 36 hours and this phase is repeated every 29.5 days.
That is, sometimes you see this full moon phase first in Germany and sometimes the moon has already set in Germany at this time and you can see the full moon phase in the USA in front of us