A second coat of stain over the lighter area might help. Rubbing a thin coat of water over the lighter area and allowing it to dry before staining might make it soak in more stain.
You could try this on one board where the new meets the old.
Another option would be to apply a tinted coat of poly to the lighter area after a clear coat has been applied but try the second coat of stain first.

Did the lighter area in the picture get sanded and stained with the darker area?

There is def a big difference between the two.

I agree with JFC that you should try to restain the lighter area first, and then try a tinted poly coat. Re-sanding is last resort, exhaust all other options first before going the sanding route.

Yes, the lighter area was a pre-finished wood that got sanded along with the darker area (new wood) and stained all together.