What anomolies? There are NONE. You're confused. Those drawings show the hookup OUTSIDE the sensors. The NPN one connects the load to ground when it detects metal (NO) or not (NC). The PNP one connects the load to power when it detects metal (NO) or not (NC). Consequently they show the load for the NPN between power and the black wire since the black wire goes to ground when the sensor is active and they show the load between the black wire and ground for the PNP sensor because it connects the load to power when active. Those drawings are correct but they sure are confusing!
Yeah, black is not ground? Good going there Mr. Manufacturer!
And why the optocoupler? Thats only really necessary if you need complete isolation between the sensor and the control/micro board. I don't see the need for that here.
If its a short connection and not too noisy an environment, just use a small signal NPN transistor with a base resistor (10K should work nicely) and a pullup to 5V on the collector and run the collector to your micro input. With the sensor the OP stated they have, now the digital signal to the micro will be high when metal is detected, low when not. If its noisy, hang a cap to ground on the base of the transistor to act as a noise filter (0.1uF for starters but you can go higher if necessary)
Something along the lines of a 2n3904, 2n2222 or equivalent would work nicely.