It's very common to have the color differences in hardwood flooring. The UNCOVERED areas get UV damage from the sun whereas the covered areas don't.
This is the problem with direct sunlight 'hitting' the floor. If the poly has UV protections, it can only minimize the damage; not prevent it. If someone can come up with a UV Poly that ELIMINATES the damage to wood, they'd be kicking sand in the Caribbean for the rest of their life.
Refinishing the floor should 'even out' the discoloration. However, as Mannington suggests, if you want to be sure your floor is 'evenly worn' by the sun, you need to play musical furniture for the rest of your life! And as an aside, you may only get 2 or 3 sandings out of the floor until it has to be replaced. So, you're already considering the 1st sanding. In less than 10 years (at the current rate), you'll have to replace the floor and start this vicious cycle ALL over again.
So, what do you do? Unless you're going to have the same, exact setup as the previous owners when it comes to rugs and furniture, I'd refinish it. Then, I'd see what could be done to eliminate direct sunlight on the floor. The addition of low E-glass, which can filter out up to 80 of UV rays, along with that of a high-quality UV protectant Poly, you should be able to reduce your 'problem' dramatically. HOWEVER, instead of seeing the 'shadows' in 3 years, you may see them in 6 (for example.) It's not a perfect solution but maybe window over-hangs or a porch might be in order. Reflective sunlight does cause this problem but it's the LEAST intrusive manner in which the flooring is 'damaged'.
Oh, after spending a TON of $$$ to install solid, Maple hardwood flooring, the last thing I'd want to do is cover them up. I would suggest, however, that you use 'runners' and 'area rugs' SPECIFICALLY made for hardwood floors. The backing on these rugs are 'rubberized'. Try to get the rugs with the backing pre-sewn. You can buy the backing separately from the rug for LARGER area rugs but unless you have a piece of furniture, or something, on top (in a strategic place or 2), the rug tends to 'stray' off of the backing. Know what I mean? In other words, if you want to lay an area rug in front of the couch, either put the front legs of the couch on part of the rug/backing combo, or set a coffee table on part of it (or both.) That way, you have something 'holding' the rug in place on TOP of the loose backing.
If you have more specific ?'s, you know where to find me, and anyone else. My best to ya and hope this helps.