CL600 FLT CREW WAS NAVIGATING THE 'GEELA2' ARRIVAL; BUT ATC HAD EXPECTED THE FLT CREW TO ALSO BE 'DESCENDING VIA' THE ARRIVAL. A CROSSING RESTRICTION WAS MISSED AS A RESULT.

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WE WERE ON THE GEELA 2 RNAV ARR TO PHOENIX AND HAD NOT BEEN GIVEN A 'DSND VIA' CLRNC BY CTR -- ONLY A CLRNC TO CROSS GEELA INTXN AT 250 KTS AND 11000 FT. THE CAPT; WHO WAS THE PNF; VERIFIED THAT THE RESTR AT HYDRR WAS THEN DELETED. ATC CONFIRMED THIS INSTRUCTION. JUST BEFORE GEELA INTXN; WE WERE SWITCHED TO PHX APCH AND THE CTLR INSTRUCTED US TO DELETE THE SPD RESTR. JUST BEFORE HENSN INTXN; THE CTLR SAID THAT WE HAD BEEN CLRED TO 'DSND VIA' THAT ARR AND THAT WE WERE 'A LITTLE HIGH.' NEITHER THE CAPT NOR I HAD ANY RECOLLECTION OF BEING TOLD TO DSND VIA THE ARR AND INDICATED OUR CONFUSION TO THE CTLR WHO RESTATED THAT WE WERE TO DSND VIA THE RNAV ARR. WE MADE THE RESTR AT LOOSY INTXN. THE DSND VIA CLRNC MAY HAVE BEEN STATED; BUT WAS AT THE VERY LEAST NEVER READ BACK AND WAS NOT RECEIVED BY THE FLT CREW. IN TALKING WITH MANY OTHER PLTS ABOUT RNAV ARR/DEP PROCS IT HAS BECOME CLR TO ME THAT THERE IS A LOT OF CONFUSION IN GENERAL AS TO WHAT IS EXPECTED OF FLT CREWS. IT SEEMS THE MORE I TALK TO PEOPLE WHO HAVE BEEN AIRLINE PLTS A LOT LONGER THAN ME; I BECOME EVEN MORE CONFUSED ON THE SUBJECT. I KEEP GETTING 20 DIFFERENT ANSWERS FROM OTHER PLTS AND CTLRS AND PLTS WHO HAVE TALKED TO CTLRS. I FEEL THE FAA SHOULD REALLY PROVIDE SOME GUIDANCE AND TAKE AWAY THE AMBIGUITY OF THESE PROCS. MAYBE THESE PROCS SHOULD BE HARD AND FAST UNLESS RELIEVED OF THE RESTRS INSTEAD OF DOING HALF THE ARR ONE WAY AND THEN BEING EXPECTED TO ABIDE BY ALL OF IT BY THE NEXT CTLR. I FEEL THERE IS MUCH MORE CONFUSION IN THIS AREA THAN RWY INCURSION AVOIDANCE TRAINING.