Fox News guy was incorrect.
The planes that serve the executive use call signs special air mission 2800 and special air mission 2900 when not carrying POTUS or VPOTUS.
Whatever aircraft the President is on is referred to as (service - one): for example when on board a USMC aircraft of any type that aircraft changes call signs to “Marine One” - most commonly of course for the helicopter used to transport him from the WH to the AFB.
When President Bush famously landed on the CVN he did so on board “Navy One”.
Similarly, aircraft carrying the Veep re-designate to (service - two).
That thought just brought a smile - thanks! As an aside - that event turned out to be so positive for President Bush that I said to myself at the time "the media will never let up on him after this". The images were just so postive they wouldnt be able to just let them go down in history as it happened.