These are often used interchangeably and are commonly accepted to be synonyms. Both words share the sense of going beyond. However, there is still a proper, formal way to use them.
Farther is used for a physical distance. Think far away. If you could fit the words a greater physical distance in place of it, it is correct to use farther.
“Is there farther to go before we turn?”
“Is there a greater physical distance to go before we turn?”
F. Scott Fitzgerald knew how to use them.
Further can be used for less concrete notions and all that metaphysical jazz:
“Without further ado…”
“Further to your letter…”
“We’ve made further progress on the research.”
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