ExtraTerrestrial Artificial Intelligence
That's what the spaceships were. Since they were from another "planet", they were referred to as "aliens". In reality, they were robots in the form of miniature spacecrafts, but with personalities. The term "aliens" usually specifies flesh-and-blood creatures from another world. I heard a slight "rumor" several(back in the 80's) years ago, that the original plot for this movie was going to be a Short Circuit/Bicentennial Man type theme. The spaceships were going to be unused, secret government, prototype, unpiloted aircraft that came to life after Frank's desire for a miracle came about, and they came the tennants' aid. Wouldn't have been as cute, but would've worked.
"Danger's my middle name. Mine's Cornelius. You tell anyone, I'll kill you"