ATR you are actually correct.
The 747-200 *there are actualy 2 of them * becomes Airforce 1 when the push climbes on board
I do not know what the call signs are when the rest of the cronies are on board but remember it has happened only once that Airforce 1 flew back - mission un-accomplished when Kenedy was killed.
Although the new pres was on board he was not inaugurated and they had normall call -signs (if the grey matter remembers correctly)
