192.168.1.9 is the IP address of your PC on your own network; the one displayed by the danasoft thing is the "public" IP address (of your cable or DSL modem, or however you connect to the internet), and is most likely correct.
The newest one I've seen actually displays your "location" (city/state), and in my case, was also correct. This is possible because of the way big internet providers (comcast, verizon, charter, etc) assign their IP addresses based on geographic location.
These danasoft things are annoying, but ALL of the information they display (browser, IP address, operating system, location, etc) is available to ALL websites that are browsed to -- not just danasoft.