what is the name of the effect that I need?

The closest thing would be Difference Matte. That will make any identical pixels transparent. If any noise, compression artifacts, or movement in the background, like leaves blowing in a light breeze, in the MP4, Difference matte will have problems. There are almost always a lot of compression and color artifacts in MP4 files, so a clean plate that is a still image or a clean plate video will almost always have problems generating clean transparency with compressed footage. 

There I'd no such thing in AE. What you describe would be a difference keyer with advanced motion detection. Something similar could be built by combining different effects of course and you could also use stuff like content aware file to mimic such functionality, but there's not a single-click stock effect for it.

Mylenium