No, star clusters do not all have the same age. Star clusters can form through different mechanisms, and their ages can vary significantly. There are two main types of star clusters: open clusters and globular clusters.
Open clusters are relatively young and contain a few hundred to a few thousand stars. They form from molecular clouds and are typically found in the disk of a galaxy. Open clusters are loosely bound, and over time, their stars can disperse due to gravitational interactions with other stars or with the tidal forces of the galaxy. As a result, open clusters tend to have a relatively short lifespan, typically on the order of a few hundred million years.
Globular clusters, on the other hand, are much older and contain tens of thousands to millions of stars. They are densely packed and spherically shaped, and they orbit in the halos of galaxies. Globular clusters are thought to have formed early in the history of galaxies, during periods of intense star formation. These clusters are gravitationally bound, which helps them survive for billions of years. Globular clusters can have ages comparable to the age of the universe, with the oldest known globular clusters being around 13 billion years old.
So, while the ages of star clusters can vary, open clusters are generally younger and have shorter lifespans, while globular clusters are older and can survive for billions of years.