The tape isn't just plastic, it has fine particles bonded to it, which can hold a magnetic charge.
The head in the recorder sets the magnetic charge on the tape, according to the signal (which basically equals the audio signal going in) on the head as the tape goes by in record mode. An erase head clears the the magnetic charge so previous a previoius recording cannot interfere with the new.
A video signal has too much bandwidth to practically record on linear tape as you can with audio. A video tape system instead uses a rotary head to to record or play the video to the tape, with a preceding full width head, and a head called the "ACE" head after the video head. the ACE head has its own erase head to clear a path for the audio and control/timing signals, which time the movement of the tape and syncs the rotary head (the tracking control tweaks that timing). When you record video, the video sync signal of the video being recorded set the timing of the tape speed (according to the speed setting), rotary head and timing signal on the ACE head.