The two parts are common-mode chokes, two coils on a common core arranged so that the flux cancels when equal currents flow through the two coils in opposite directions. The flux adds when current flows in the same direction.
There are other ways to indicate that function such as those on this page from Coilcraft.

The idea is to present a low impedance to currents flowing through the CM choke to a load, but a high impedance when there is a voltage between the line inputs and ground. Since the load currents cancel a much smaller core can be used for the same inductance without saturation occuring.
From here is a similar filter with component values shown.

The "circular arrow" (showing magnetic flux, not current) symbol probably derives from the physical arrangement of coils on a toroidal core (back to the Coilcraft page):
