. . . Or is it the other way around?
Among other dictionaries, the Canadian Oxford (the Geist lexicon of choice) considers the two words interchangeable, as they have been for centuries. Further is preferred in the Oxford, and farther is shown as a variation.
In North American usage, though, farther is gravitating to passages that refer to physical distance (“They walked a bit farther”) and further to those that refer to extent (“They did not take the matter any further”).
We know a couple of writers who insist on further, believing that farther is more American. Statistically that may be true, but both words have solid pedigrees. Further came first, in Old English as the comparative form of forth; farther, a variant, appeared in Middle English, and the two have made their merry way into the present time like identical twins — they have subtle differences, but few people can tell them apart and almost no one minds.
H.W. Fowler, author of Modern English Usage (which, when it was published in 1926, was more modern than it is today, but that old edition is still a joy), declared that “hardly anyone uses the two words for different occasions; most people prefer one or the other for all purposes. . .” But even then, eighty years ago, he noted that perhaps farther got used more often in reference to distance.
How does a writer decide which to use? Either word is correct. Some writers strive for consistency; others go with the distance/extent principle. When the document gets edited for publication, the editor recommends that the writer apply the publisher’s stated preference.