I stand corrected: I did not remember that Executive One also sometimes refers to military helicopters when a former president is on board. In my mind it was reserved for civilian fixed-wing airplanes that carry (the only) POTUS, and I assumed KDCA tower was talking to an aircraft at Reagan. As Trump did not leave Washington with his private plane on January 20th and Obama took a military airplane to California with the call-sign Special Air Mission (SAM) 44 from Andrews, none of this made sense.
So: Obama took off from Capitol Hill in a military helicopter with the call sign Executive One, KDCA tower waved good-bye (and halted traffic) from the other side of the Potomac, Obama took off from Andrews in a military airplane with the call sign SAM 44. And Trump stayed in Washington.