As others have noted, English uses the same word for both concepts. Cornbread and Chaos suggest distinctive words, but they wouldn't be immediately recognized as having the meaning sought. ("Cornbread and Chaos" -- sounds like a band melding country music with heavy metal.) So they're fine if you are writing a long discussion and it's reasonable to introduce your own terms and define them, but you couldn't just use them without explanation and expect people to understand what you meant.
Thus, if you want to distinguish them, you need to add some adjectives or reword the sentence.
In many cases it would be obvious from the context. If you said, "Fred kept his pilot's license in his blue suit", that would clearly indicate you are talking about a card or certificate. If you said, "Fred became a licensed pilot in 2008", the reader would likely understand that to mean that he met the official requirements. But I can imagine statements that would be ambiguous. Like if you said, "Fred lost his pilot's license", does that mean that he misplaced the physcial document, or that his license was revoked by the authorities because he broke the rules or some such?
I think if you said "physical license", "license card", or "license certificate", people would understand you to mean the piece of paper or plastic or whatever. If you wanted to make clear you were referring to the concept, I think you'd need a longer construction. Like in the "lost" example, you could say, "Fred lost his license card" to mean the physical object. To make clear that you are referring to the concept, you'd have to say something like "Fred's license was revoked" or "Fred lost his right to pilot an airplance". I really can't think of any adjective you could slap on to identify the concept.