Small Aircraft; Low Wing; 2 Eng; Retractable Gear
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 17
Communication Breakdown; Confusion; Situational Awareness
Conflict NMAC; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Air Traffic Control Separated Traffic
Procedure
I was instructing on ARS/ARN combined.  Aircraft X departed and requested vectors for ILS (VFR).  Developmental assigned heading; 5000; and maintain VFR to Aircraft X.  Aircraft Y departed on a similar route as Aircraft X.  Prior to communication change to our frequency; Developmental called local control and requested them to assign Aircraft Y 4500ft.  When Aircraft Y did report on frequency he reported 'at 4500.'  Developmental issued traffic to both aircraft.  Aircraft Y reported Aircraft X in sight.  Aircraft X was still looking for Aircraft Y.  Shortly after Aircraft X was issued a turn for the ILS; he reported a NMAC with Aircraft Y.  After reviewing the tapes;local control issued 'at or above 4500' to Aircraft Y.  Aircraft X altitude did indicate as low as 4800 after targets merged.Reissuing 4500 to Aircraft Y seems a bit redundant but possibly could have changed the outcome.  Reissuing traffic to Aircraft X because he didn't have him in sight might have changed the outcome.  Reissuing 5000 to Aircraft X after seeing his altitude change might have changed the outcome.
BOI TRACON Controller reports of two aircraft that were in conflict although both were VFR.