I am not familiar with this terminology screen core. 30 years ago all the 110/120VAC solenoids I worked on were two wires. We evolved int three wires, one for ground, because if the hot wire shorted to the solenoid case, it would make the case hot. If the case was not grounded anyone touching it would be shocked. It makes a lot of sense for safety. As the solenoids were replaced over the years I have run into places where the green wire was terminated on the ground screw on the conduit. I don't know if this will meet code today, it is a safety issue if the conduit is not grounded. The systems I see today all have three wires for 100vac. But I run into very few of these because most systems have switched to 24VDC solenoids. The best is to check the local code. What was acceptable years ago is often a no no today.
Mark