PSAV = PSA velocity.

PSA velocity focuses on the absolute change in PSA per unit of time (ng/mL/year).
PSA doubling time focuses on the time required for PSA to double, reflecting more of the "growth rate" of PSA levels.

From what I understand PSA velocity is used more in detecting early trends in PSA changes, for example when screening or monitoring low-risk prostate cancer. PSA doubling time is used more after treatment (e.g., prostatectomy or radiation) to assess a cancer's recurrence or aggressiveness.

PSA Velocity