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<stdexcept>: Defines a set of standard exceptions that both the library and programs can use to report common errors. -
<exception>: Defines the base class (i.e.,std::exception) for all exceptions thrown by the elements of the standard library, along with several types and utilities to assist handling exceptions.
So, <exception> only defines the class std::exception, while <stdexcept> defines several classes that inherit from std::exception (e.g., std::logic_error, std::out_of_range). That is why <stdexcept> includes <exception>.
They are in separate headers because if you want to define your own exception class inheriting std::exception (and not use the classes from <stdexcept>), you can avoid unnecessary definitions.