What the statement *means*:
The statement is trying to say that a star gravitationally bound to another star can be part of two different types of systems:
* A star cluster: A group of stars gravitationally bound together. These clusters can be open clusters (loosely bound with a few hundred stars) or globular clusters (tightly bound with hundreds of thousands of stars).
* A binary star system: A system of two stars orbiting around a common center of mass.
The problem with the statement:
The statement implies that a star gravitationally bound to another can be part of either a cluster *or* a binary system, when it's actually possible for a star to be part of both.
A better way to phrase it:
"A star gravitationally bound to another star can be part of a binary star system, and a binary star system itself can be part of a star cluster."
Examples:
* Binary star system within a cluster: The star Mizar in the constellation Ursa Major is a binary star system, and both stars are part of the open cluster known as Ursa Major Moving Group.
* Cluster of binary stars: Globular clusters often contain many binary star systems.
In conclusion:
While it's true that a star bound to another can be part of a binary system or a cluster, the distinction is that a binary system can be a component of a larger cluster.
