The circumstances when I use this analogy are mostly language evolution, borrowings, and their overall impact on a language. I’ll use two English example sentences to demonstrate this:
I adore their potatoes with jerky, amigo.
*Apple me eats two.
Which one of those sentences is recognisably English? It’s the first one because, while it’s full of borrowings*, it still abides to the morphological and syntactical rules of the language. In the meantime, the second sentence is rubbish, even if it uses well-established native vocab - because it doesn’t abide to English syntax and morphology.
Or, by the analogy: the first sentence might’ve changed the fur of the beast, but the beast inside is still the same. The second one plopped that beast’s fur over something else, but the beast isn’t there any more.
(The “pronunciation” / phonology is a third can of worms. It doesn’t work well with the fur vs. beast analogy.)
*“adore” from French, “their” from Old Norse, “potato” from Taino, “jerky” from Quechua, “amigo” from Spanish. Only “I” and “with” are native.