Core RAM =/= Core ROM

They work using completely different principles.

Core RAM used ferrite cores as the bits, with the wires used to magnetize the cores in opposing directions (clockwise vs counterclockwise; '1' vs' '0').
(Little memory moment here - the ferrite cores would break and fall on the floor.  Your sysadmin would sweep up the detritus, and put it in the bit-bucket. (see?  there was a literal explanation!!!)

Core ROM uses ferrite cores as transformers, with the wires themselves being the bits.  The ferrite core would be used to induce a current (or not!) in a second wire based on whether there was a current in the first wire (if the second wire was wrapped around the core too, the current would be induced.  If it wasn't wrapped, no current.  See?  '1' vs '0'!
(Mind you, you could, theoretically, flip a bit by moving/rewrapping a wire!)

To think this is the stuff that got people to the moon and back :-)