When their STAR was changed to the GRIZ 3 by ATC the Flight Crew of a CE560 selected the chart for the west runways instead of the one for the east which were actually in use.

Narrative

While descending into Vancouver on the Paine Arrival; ATC reassigned us to the Griz Arrival. We pulled out the Griz Arrival plate and noticed how this new arrival was directing us to the west runways; even though they were still using Runway 8 in Vancouver. This felt odd; but we thought ATC must have their reasons to change us to this arrival.When entered in the FMS; the RNAV points didn't match up with the chart until we changed the arrival runway to 26. That should have been our clue. When we turned to a 290 degree course after Egret; ATC questioned us after about 3 miles if we were on the Griz Arrival going direct to TATGO. We told him to standby; and after about 5 seconds he said 'never mind; just go direct YVR VOR'. We looked again through the arrival charts; and there was another STAR in there with the identical name (Griz3); the only difference was this one was going to the opposite side runway. The course after Egret on this arrival was 293 degrees vs the 290 we were on. The Controller never said anything else about it.We should have realized that something just didn't feel right and investigated further; but it honestly never occurred to me that they could have 2 STARs of exactly the same names with different RNAV points on it. Maybe they should rename one of them; but I will definitely be watching out for this in the future.