The casting of a thing onto a surface, and the extending of a trend into the future. Both show something not actually there.
Latin projectio (a throwing forward), from proicere: pro- + iacere (to throw); a projection casts an image or a trend onto a surface that does not itself contain it.
The casting of something not present onto a surface where it can be seen — an image thrown on a screen, or a trend thrown forward into a future that has not happened yet. Both show something real about the source and nothing certain about where it lands.