NCLEX is a national exam administered by the National Council of State Boards of Nursing. You can take the NCLEX in any state and have it count towards any one state licensure.
However, all states do not share licensure reciprocity. Only states participating in the Nursing Licensure Compact Act allow RNs and LPNs to have immediate reciprocity. Check out this website for a list of states participating in the Nursing Licensure Compact Act: https://www.ncsbn.org/158.htm
All other states require that you specifically apply for a license in their state (which usually includes a application fee, background check, and nursys.com license verification).
As for the 'one year' experience thing. I think it depends on the hospital/position for which you are applying. Some specifically say 'one year acute care exp.' or 'one year hospital exp.' I've seen others that simply say 'one year nursing exp.' So, it all depends..
Hope that helps!