While common magnetic tape uses very thin, plastic-coated iron oxide, "talking rubber" uses rubber impregnated with iron oxide. Iron oxide (a form of rust) is ferromagnetic, which means in the presence of a magnetic field, the electrons in the iron oxide magnetically line up and stay that way even after the magnetic field is turned off. This allows cassette tapes to create a “track” of magnetically aligned iron oxide when the electromagnet in a cassette recorder creates a magnetic field.
But with magnetic rubber, the iron oxide is actually mixed into the rubber material; the whole band becomes ferromagnetic, instead of just the coating. According to that Bell System Journal article, this “talking rubber” could be around 1/16 or 1/8 of an inch think, whereas magnetic tape was (even in the '50s) already much thinner at 1/1000 of an inch thick.
More obscure audio formats!