From the cplusplus.com reference for <exception> and that for <stdexcept>, it appears that <exception> is sufficient for exception handling in C++98 or higher versions of C++.
Why does C++ have two headers files for exception handling? How does this affect my development? Which header should I use?
The Standard does not require that <stdexcept> includes <exception> at all.
C++ Library - <stdexcept> It is an exception classes and this header defines a set of standard exceptions that both the library and programs can use to report common errors.
C++ provides a list of standard exceptions defined in header <exception> in namespace std where “exception” is the base class for all standard exceptions. All exceptions like bad_alloc, bad_cast, runtime_error, etc generated by the standard library inherit from std::exception.
An exception in C++ is thrown by using the throw keyword from inside the try block. The throw keyword allows the programmer to define custom exceptions. Exception handlers in C++ are declared with the catch keyword, which is placed immediately after the try block.
<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.
One practical consideration is that <stdexcept> requires std::string definition  (exception constructors accept std::string and have std::string data member), whereas to catch and query std::exception std::string declaration or definition is not required. 
In other words, std::exception handler only needs <exception>. The throw site requires the header of a particular exception class it throws.
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