NAT stands for Network Address Translation. This is where in most cases a "private" address (i.e. RFC1918) is mapped/converted to a publicly routable address.
Double NATing from what I have run into is where you start out with say 10.1.1.5 address and it is NAT'd to 12.37.160.33 when you pass through the first firewall. When you come to another firewall, 12.37.160.33 would then be NAT'd to yet another address of 68.23.122.54. Not ideal but it has been known to happen. In my earlier days of networking, Double NATing was a bad thing and prone to having problems. With improvements over the past couple of years, having problems with Double NATing doesnt seem to be the problem it has been in the past.
I think Double NATing and NAT overlapping from what you are asking are the same thing.
Ron
