What are the similarities and differences between domestic and global project management?

Depends whether you mean working a global project that involves various countries, or project management in countries other than the US.

In general project management is similar the world over, although in the US the Project Management Institute is more well known than in the rest of the world where the IPMA is more known. In the UK in particular the PRINCE2 process/certification is well known - less so in the US.

Some domestic projects can be spread over many states, which presents many of the same challenges as different countries. However, international projects obviously have the additional challenges of language, customs/import/export issues, local laws, local customs, security, exchange rates, wider time differences, travel costs, international treaties etc.

well, domestic management concerns political hypocrisy. global management is more the game of chess, ending with the burdon being laid at the feet of others who have even others underneath them to blame. sad but true, this answer it is.