I'm not too familiar with Tae Kwon Do, but from what I've gleaned over the years, their front stance is different from ours in that:
- the lead knee is still bent, but straight forward, not angled "in"
- both feet face forward, not angled in
- their stance is more diagonal than forward, making for a wider, shallower stance
Here's an impressive schematic:
http://tkdtutor.com/09Techniques/Stances/StanceTechniques/Front/Front01.htmAs Jared noted, the Tiger front stance is maximized for stability, defense and power generation. By contrast, the Tae Kwon Do front stance is wider, more open, and less defense-oriented.
As always, just for fun, looking at the context might shed some light. Look at each of the technical differences, and see how they might maximize the stance for the situation it's built for. Tiger is a 2nd gate fighter concerned with holding ground and doing damage; Tae Kwon Do is concerned with moving at 3rd gate and making contact with fast, long-range attacks. Close range combat vs. long range sparring. How do the differences in front stances factor into that?
Granted, Tae Kwon Do in the U.S. usually means tournament sparring, but this doesn't even have to amount to the usual, silly "They train for sport and we train for REALS, yo!" scoffing you see in martial arts. One front stance would work great in an empty parking lot; the other, in a cramped hallway. No one fights in a vacuum.
This whole train of thought might offer an answer to Jared's chicken/egg question, but that's another discussion altogether.