Both kinds of generated class store every parameter as std::decay_t< type > member_<name> and expose it through std::decay_t< type > const &<name>( ) const.

StreamableException
name<Name>Streamable<Name>Exception
storedparametersinternal_locale, parameters, internal_what (not with OVERRIDE)
constructors( params )( params, loc ) if needed, ( params )
explicitwith one parameterthe non-locale constructor, with one parameter
destructorvirtualvirtual
textPrintOn( std::ostream & ) const, operator<<What(), what() noexcept — or the OVERRIDE method
baseINHERITED, default-constructedINHERITED, default-constructed

The member order is the declaration order above; an exception's layout is therefore locale, parameters, cached text.

Getters return a const reference to the stored value, so a getter of an std::string const & parameter returns std::string const & — valid as long as the object lives.