Historically, these words have been interchangeable with regard to distance, but further is the preferred choice for the adverb meaning "moreover," the adjective sense meaning "additional," and as a verb ("to further one's career").

Adverb: both words mean “more distance,” but only further can also mean, “additionally” (short for furthermore). Adjective: both words work as the comparative form of far, but only further can also mean “additional.”

It’s used mainly just to add one piece of information on a subject to another piece of information on the same subject. “Furthermore” does the same thing, but it is more emphatic in tone. It sends out a little bit stronger signal to the listener or reader that says: “Stay with me!