Do the terms "Airprox" and "Near mid-air collision" mean the same? If not what is the difference between them?
A Near Mid Air Collision (NMAC) is an Aircraft Proximity (AIRPROX), but an AIRPROX is not necessarily an NMAC. NMAC is used by the FAA (see 7-6-3 in the AIM), while AIRPROX is used by ICAO.
NMAC is empirically defined as coming within "100 feet vertically and 500 feet horizontally" of the other aircraft, whereas AIRPROX is categorized from A to D. The A to D categories are not empirically defined.
A - Risk of collision.
B - Safety not assured.
C - No risk of collision.
D - Risk not determined.