Thematically, the Fighters Guild is a group of professional mercenaries for hire. The undaunted are a bunch of people who share a common interest - going into the nastiest places in Tamriel and kicking ass.
Fighters Guild = Warriors and soldiers who want to be the best at what they do and offer their services in defense of the innocent etc. etc.
Undaunted = Drinking buddies who like to get really drunk and do something stupid, like charge off to fight the biggest, baddest unholy creature they can find just so they can brag about it later.
"He who fights with monsters should look to it that he himself does not become a monster...when you gaze long into the abyss the abyss also gazes into you..."
The Fighter's Guild are contract mercenaries who undertake officially-sanctioned work (at least by virtue of having a charter authorizing them as a guild for the purpose). They don't - at least as a guild - engage in freelance adventuring.
The Undaunted, on the other hand, are all about freelance adventuring. They aren't a guild, they don't have a legal charter, and they don't seem to contract their services out to others.