Small Transport
Air Traffic Control Fully Certified
Confusion; Situational Awareness
ATC Issue All Types; Conflict NMAC
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Aircraft; Human Factors
Aircraft X was southbound at 3;000 feet. There was a VFR aircraft northbound at 3;000 feet. I called traffic and issued a right turn to avoid. A moment later; I was on the landline. While on the line; Aircraft X calls that he is taking evasive action due to a VFR aircraft. I did not issue a traffic alert since the pilot was already maneuvering. I initially thought that the VFR traffic was the previously called traffic. Upon later review; I saw that it was actually a different aircraft. The VFR was southwest of Aircraft X; southbound at 4;700 feet. The VFR aircraft made a fast; right descending turn towards Aircraft X. I never saw the VFR aircraft make the turn; and I don't remember [a] conflict alert going off prior to me be being on the landline. I have no specific recommendations. However; if the adjacent TRACON STARS had a feed with our STARS system; inbound information could be handled via automation rather than landline coordination. This may have given me enough time to see the event develop.
JAX TRACON Controller reported an aircraft had a NMAC with another unidentified VFR target that the Controller confused for other VFR traffic.