Air taxi jet Captain reported a near miss with another aircraft while taxiing at a tower-controlled airport. The Captain was focused on ground control advisory traffic and did not see another aircraft of the same type exit the runway in front of the Captain's aircraft; passing by; then continued safely to the ramp area.

Narrative

Landing 7R PHX and cleared 7R at H6. Tower advised taxi to FBO X on Hotel; monitor ground 132.55. Prior to our landing Aircraft Y had landed and was taxiing to the FBO X. We were aware of this aircraft. Proceeding west on Hotel; we heard Aircraft Y state he had taxied to FBO X by mistake instead of FBO Y…and asked to repo to FBO Y. PHX ground cleared the aircraft onto Hotel. Ground control asked us if we were up" and we acknowledged. Then ground controller said pass behind Aircraft Z exiting on Hotel. We only knew of and were looking down the taxiway at the repo aircraft and we knew we were well clear of him and would pass behind as opposite direction traffic. However ATC was referring to a different aircraft; Aircraft Z; that had been cleared by the tower to exit H4 onto Hotel to the ramp. As such we were approaching H4 westbound and taxiing at normal speed when we suddenly saw the aircraft exit 7R on H4 at a high speed and turn in front of us onto Hotel. It was close and startled us as we were looking at the repo aircraft going to FBO Y; not at the runway. I commented to my FO (First Officer) we should have been instructed to Hold short of H4 for aircraft exiting the runway vs the ambiguous previous instruction. Well it bothered me all night as we could have easily had a collision at H4. I called the PHX tower supervisor this morning to discuss and relayed my startle and concern. He later called and verified the ground controller only said pass behind the aircraft exiting onto hotel but conceded that it could have been Aircraft Y or Aircraft Z. He said the controller should have stated pass behind Aircraft Z exiting 7R at H4…learning experience for all. Obviously; although taxiing into the ramp at the end of a long day; we let ourselves get fixated on the wrong aircraft; and we did not confirm the aircraft we were looking at. Also we usually are cleared to the ramp to stay with and monitor tower; the only way to know of the conflicting aircraft exiting H4.Cause: Incomplete instruction from ATC for traffic exiting RWY 7R; our failure to confirm where the aircraft was coming from ramp or runway; fatigue; and distraction. Tower supervisor advised we were separated by 420 ft. This could have been a catastrophic event. No violation of clearance; however reporting for pilot awareness and lessons learned.Suggestion: Full attention to the runway and intersecting taxiways until parked at the ramp…confirm;confirm;confirm especially in light of ambiguous communication"