No crank no starter buzzing noise? Starter not working

Was driving my car one day and it turned off at a stop sign (full stop). Was able to start it right back up. Vehicle was fine for a few days. Drove it again for several miles and when I went to start the next morning if would not. Car will not start in neutral. Dash lights up fine. The battery is three months old and fully charged (had triple A came and check it out). Engine grounds are fine (checked with multi-meter). Replaced the ignition switch and the problem remains. The starter relay under the dash vibrates/buzzes loudly when I try and start the vehicle. The engine will not crank.

Question: Does it make sense that the relay would be buzzing if it were bad? I assumed it was because it was not getting any power but when I replaced the ignition switch the problem remains. Are these symptoms of a bad starter? And would a bad starter cause the car to fail while at a stop sign? Just trying to check these questions off the list before I have it towed. Thanks very much.