some correlations between the two, they are not the same.
The "which state you belong in" test is apparently based on a few items from the big five inventory.
I looked over the JPSP article presenting the actual research. They had two samples in which participants did the big five, two that did a ten-item version with sometimes iffy reliability (this may be the same test used in the "which state" test?), and one that completed a different measure. It's really not my field of expertise so I can't comment on the research itself, but I was surprised that the authors did not discuss possible limitations of their work.
Anyway, I got New Mexico. I don't think I belong there.