What are the differences between C/C++ bare-metal compilation and compilation for a specific OS (Linux)?

Suppose you have a cross-compilation tool-chain that produces binaries for the ARM architecture.

Your tool-chain is like this (running on a X86_64 machine with Linux):

• arm-linux-gnueabi-gcc.exe : for cross-compilation for Linux, running on ARM.
• arm-gcc.exe : for bare-metal cross-compilation targeting ARM.

... and the plethora of other tools for cross-compilation on ARM.

Points that I'm interested in are:

• (E)ABI differences between binaries (if any)
• limitations in case of bare-metal (like dynamic memory allocations, usage of static constructors in case of C++, threading models, etc)
• binary-level differences between the 2 cases in terms of information specific to each of them (like debug info support, etc);

• ABI differences is up to how you invoke the compiler, for example GCC has -mabi and that can be one of ‘apcs-gnu’, ‘atpcs’, ‘aapcs’, ‘aapcs-linux’ and ‘iwmmxt’.
• On bare-metal limitations for various runtime features exists because someone hasn't provided them. Be them initializing zero allocated areas or providing C++ features. If you can supply them, they will work.
• Binary level differences is also up to how you invoke compiler.

You can check GCC ARM options online.