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.

The principals are the same (planning, communication, tracking etc) but you have to be much better at the communication and make more of an effort to to call people rather than rely on email to keep the relationship working.
Also obvious things like arranging meetings that are common for multiple time zones.
Also be concious of cultural differences and how that may effect peoples behaviour.