The side that can be switched on by itself is the battery; the side
that is physically interlocked to turn both sides on when activated is
the alternator. The idea is that you can have the battery on without
the alternator, but you can't have the alternator on without the
battery.

The battery side controls the coil of the master solenoid, and thereby
connects the battery to the main power bus. The alternator side
switches the power to the alternator field coils, typically via the
voltage regulator and over-voltage relay, and thereby effectivly
switches the alternator on or off.