4 of 4 Address comments.

The short answer is that you’d expect lib to be built (or rather, installed) if there’s a library to install, and include if there are headers to install. Usually the two go together (at least for C and C++ libraries).

In binutils’ case, the libraries and associated headers are libbfd and libopcodes, as you mention. libbfd is a library used to manipulate object files in a variety of formats, libopcodes is a library used to map opcodes to instructions. libbfd is installed by default for same-host compilation, but not for cross-compilation, which is why you’re seeing different behaviour in your scenarios. You can see the conditional default in bfd/acinclude.m4 in the source code. Both libraries should be built in all cases.

You only need libbfd if you want to build GDB. If you do want to install it in a cross-compilation scenario, you can tell ./configure to do so with the --enable-install-libbfd option; when you do this, the libraries and header files will be installed in the appropriate host- and target-specific directory (libbfd is built for the host but contains target-specific code).