First, let's talk about their interchangeability. There are some contexts where the two words could be used to mean "additional"; however, I think there seems to be a subtle difference in meaning when the word further is used:
The summit ended without any more talks.
The summit ended without any further talks.
I could not have run any further.
I could not have run any more.
In the case of the summit meeting, the word further hints that talks might have helped two sides come closer to an agreement. That's because one meaning of further is:
further (adv.) at or to a more advanced, successful, or desirable stage
In the case of the tired runner, any further suggests a greater distance, while any more suggests a longer time. While those meanings overlap, I think further might be a better word for a runner dropping out of a marathon, while more might be a better word for someone working out on a treadmill. That's because further also means:
further (adv.) by a greater distance, or for a longer way
As for the book, I think the best way to describe the latest edition of a book is:
a new edition of the book
You might use another when comparing two different editions of the same book:
I bought a new copy of A Study in Scarlet.
Really? I thought you already owned that book.
I do, but this was another edition.
It's harder to use further, because, in the context of publishing, I would interpret further to mean:
further (adj.) additional to what already exists or has already taken place or been done
However, I suppose we could:
The publisher has indicated a reluctance to print any further editions of this book.
In that last sentence, the adjectives new or more could work in place of further.