Nokia Lumia 822 - What are the differences between the Contacts Transfer app and Transfer my Data app?

Contacts Transfer is only available for Nokia Lumia with Windows Phone 7.x. 

Transfer my Data is the evolution of Contacts Transfer for Nokia Lumia with Windows Phone 8 and beyond.

Transfer my Data also supports transferring contacts with an SD card if the contacts were saved on the card in a compatible format and your phone has an SD card slot.