"right traffic pattern" vs. "right-hand traffic pattern" Is it officially called "right traffic pattern" or "right hand traffic pattern"? I'm mostly interested in EASA terminology, but also FAA / other areas of the world.

Background: After I always said "right-hand traffic pattern" on frequency I got feedback from other pilots that I should leave out the word "-hand" to keep communication on frequency on a minimum - so I was now wondering, if there is any official terminology for that to be used. When looking in the Eurocontrol Phraseology Database, I only found "right hand pattern" for holding patterns.
"Right traffic pattern" and "right hand traffic pattern" are one in the same.  Usually on the radio either a controller or a pilot will abbreviate it to simply "right traffic" to expedite radio communications.  

For example, A C-152 student pilot is inbound for a controlled airport and says something like "Plainview Tower, Cessna one two five X-ray ten miles to the south at two thousand, inbound with ATIS Golf."  If a controller wants a student pilot to fly a right traffic pattern to land on runway 16 which is active, they might say something like "Cessna one two five X-ray enter right downwind runway 16.  Report abeam the tower."  The pilot then responds reading back the instructions to the controller and might say "right downwind one six.  Report abeam.  Two five X-ray."