This paper investigates an intelligent reflecting surface (IRS) aided millimeter-wave integrated sensing and communication (ISAC) system. Specifically, based on the passive beam scanning in the downlink, the IRS finds the optimal beam for reflecting the signals from the base station to a communication user. Meanwhile, the IRS estimates the angle of a nearby target based on its echo signal received by the sensing elements mounted on the IRS (i.e., semi-passive IRS). We propose an ISAC protocol for achieving the above objective via simultaneous (beam) training and sensing (STAS). Then, we derive the achievable rate of the communication user and the Cramer-Rao bound (CRB) of the angle estimation for the sensing target in closed-form. The achievable rate and CRB exhibit different performance against the duration of beam scanning. Specifically, the average achievable rate initially rises and subsequently declines, while the CRB monotonically decreases. Consequently, the duration of beam scanning should be carefully selected to balance communication and sensing performance. Simulation results have verified our analytical findings and shown that, thanks to the efficient use of downlink beam scanning signal for simultaneous communication and target sensing, the STAS protocol outperforms the benchmark protocol with orthogonal beam training and sensing.