Well, in a Christmas story, an elf is often a symbol of magic and help. If it's 'elf from elf', perhaps it could mean a lineage or a connection between different elves within the story's universe. Maybe one elf is descended from another, or they are part of a special group where the actions of one elf influence or are related to another elf. For example, in some Christmas stories, an older elf might train a younger elf, so the younger elf is 'from' the older one in terms of knowledge and skills.
In many Christmas stories, the elf is a key character. For example, in some tales, elves are the ones who make all the toys in Santa's workshop. They work day and night to ensure that there are enough toys for all the good children around the world. They have special skills like woodworking and sewing, and they add a touch of magic to the Christmas narrative.
The elf in 'A Christmas Story' is part of the Christmas - themed elements in the story. It might be seen in the context of the family's Christmas experiences, like in the store displays or as part of the holiday decorations. But we don't really get a lot of individual backstory for this elf character, so it's mainly there to enhance the overall Christmas atmosphere of the story.
Definitely not. 'A Christmas Story' and 'Elf' are different movies with no character crossover. Ralphie is unique to the former and has no presence in the latter.