The elf.h file defines standard ELF types, structures, and macros.
gelf.h file defines generic ELF types, structures, and macros.
Could you please provide the standard and source documents
elf.h comes from the glibc project:
gelf.h is part of the libelf api which is a common library implementation shared between various unix-like system. It doesn't have a formal standard but the implementers (elfutils GNU/Linux, Solaris, BSDs, etc) coordinate any extensions.