A private terminal is a smaller terminal in a different location than the main terminal. The private terminals are used for private planes. We don't fly private planes. We fly regional planes, however, they still meet the size requirements to take off and land at private terminals. There are never any lines and they have their own security system. So you can show up 15 minutes before the flight and still make it.

Is this the Private Suite at LAX?

No TSA security. No big-airline check-in lines.

Immigration doesn't apply on domestic flights anyway.

The site says the terminal still has TSA security, which makes sense, these aren’t exactly private jets.

Which is a bit curious as it sounds like a GA terminal, which generally just have a guard who keeps random people from walking around on the tarmac.

But i'm guessing they are trying to be in the grey area between being a charter and being a full blown commercial airline service with a regular schedule, requiring them to use the normal passenger terminals (and lease/buy gate space/etc).

Yes. It usually does. Also at some airports customs is seperate as well.