The use of the puzzle piece to represent Autism was first introduced in the 1960's, by Gerald Gasson. A puzzle piece was chosen because Autism was thought to be a "puzzling condition." The logo first included a crying child, but was later replaced with bright colors instead. The significance of the logo was to imply that Autistic people had something "missing" that had to be ractified or found. Autism Speaks later adopted the logo, opting to make the puzzle piece blue to represent the false notion that Autism occurs more in boys.
On the other hand, the infinity symbol was made by and for Autistic people. The infinity symbol was chosen to represent neurodiversity, with infinate variations and infinite possibilites. It is a celebration of the beauty of the differences of Autistic people. There are two main versions of the symbol-- one rainbow, and one gold. The rainbow signifies the diversity of Autism as a spectrum, while the gold cleverly comes from the fact that the chemical symbol for gold on the periodic table is "Au."