Express Post International is the USPS term for EMS. It's the exact same thing.

Australia post do handle EMS - although as STL said, a lot of it is done through AAE (which is a joint venture between Australia Post and Qantas, using the resources of both). Whether or not EMS is delivered by your local postie depends on the contracts in the area - some postal delivery areas have contractors who only do regular parcel delivery, in some they do it all.