Is the RC12YC the same as the RC12YX spark plug?

Not really, but that is the only plug Sears sells as a substitute. The RC12YC plug looks like it was designed for a gap of 0.035-0.040", while the RC12YX plug was clearly designed for the recommended 0.020" gap. The RC12YC electrode is a fat cylinder like most spark plugs, while the electrode of the RC12YX is cut down to about half of the diameter. I'd guess the special RC12YX makes it easier to start the engine on a single pull.