OK, here's how it works. I just had a static IP address added yesterday.
I was using "private" to describe the "10", "172.16-31", and "192.168.0-255" ranges, which are also called "non-routed".
Without a static address, your PCs only see the 192.168.0.something address that is supplied via NAT from the modem. The modem has a public address that is dynamic. In my case, the public address was 97.something.
With a static address, your PC or router will see the public address. In my case the static address is 174.something.
It is not supported to have the modem pass through (bridge) the public address unless you buy a static IP address. This is different than both of my other internet services. In those other cases, I have a dynamic address that is assigned directly to the computer or router which is attached to the modem. Since my other two internet services DO allow public addresses to be passed even though they're dynamic, I suspect this is a marketing way for HughesNet to bump us up two plans, and get ten bucks for a static address.
I also had a previous wireless internet service where the IP address that I saw was a 10.something address. They were NAT-ing many users through a single DSL upstream connection.
So, to summarize - unless you rent a static IP address, the HughesNet modem will only operate in NAT mode, and your computers will not have visibility to the public address.
The reason I cared, and the reason this is important, is that it's much easier (at least for me) to set up inbound routing for cameras and computer services directly, rather than with doubled NAT.