The age of the solar system and the age of the Sun are indeed different due to the way they formed.
The solar system formed approximately 4.6 billion years ago from a giant molecular cloud composed of gas and dust. The exact process of how the solar system formed is not completely understood, but scientists believe it began with the gravitational collapse of a small portion of the cloud, called a nebula. As the nebula collapsed, it started to spin and flatten into a spinning disk. Most of the material collected at the center to form the Sun, while the remaining material in the disk clumped together to form planets, moons, asteroids, and other objects.
The age of the solar system is determined by the oldest known objects within it, such as the Moon rocks brought back by the Apollo missions, which have been radiometrically dated to approximately 4.5 billion years. This age represents the time when the solar system's solid bodies, including the Earth and the Moon, began to form.
On the other hand, the age of the Sun is determined using different methods. Scientists study the ages of nearby stars similar to the Sun by examining their properties and evolution. By analyzing the life cycle of stars and their formation rates in our galaxy, astronomers estimate that the Sun is around 4.6 billion years old, slightly older than the solar system itself. This difference in age arises because the Sun formed from the collapse of a specific region within the larger molecular cloud, while the rest of the cloud continued to evolve and eventually gave rise to the solar system.
It's important to note that determining precise ages of celestial objects can be challenging and relies on various assumptions and measurements. However, based on current scientific understanding, the solar system and the Sun have slightly different ages due to the specific processes involved in their formation.