Did Joe Biden get on the wrong plane?

Prisoners who were locked up in other countries finally returned home in a historic prisoner swap/release. But once things were settled and people were welcomed home, Joe Biden was spotted getting on a plane. Was that the plane that just flew in with the prisoners? Did Joe Biden get on the plane when he wasn't supposed to? Where was he going? Can anyone confirm this one way or the other? Are we just as confused as Joe Biden might have been?