Communication Breakdown
ATC Issue All Types; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert
Human Factors; Procedure
On arrival to runway 35L transition we were told by Edmonton Center to descend and maintain 12;000 feet. Prior to receiving this altitude clearance we were given no other instructions on altitude such as 'descend via the arrival;'  'cross ZZZ at 13;200 feet and then maintain 12;000 feet or even 'comply with the published altitudes on the IGVEP3 arrival.' At approximately the time we were crossing TULOS on the arrival we were told to stop our descent at 13;000 feet (even though we had previously been cleared to 12;000 feet). We were then informed that we needed to comply with the altitudes on the arrival even though we were given no such clearance and had been previously cleared by Edmonton Center to descend and maintain 12;000 feet.The root cause of this event is a difference in terminology between the U.S. Air Traffic Control and the Canadian controllers. After we were cleared to descend to 12;000 feet we were under the impression that we should descend and maintain 12;000 feet.If there is a difference in procedure between the 'descend via' clearances in the United States and Canada; all pilots operating between the two countries should be made keenly aware of the differences before operating in Canadian airspace; perhaps by way of a notation on the dispatch release or in the '10-7' airport familiarization chart.
CRJ-700 Fist Officer reported confusion on altitude assignment on arrival to CYYC; citing differences in U.S. and Canadian ATC terminology with respect to 'descend via' clearances.