How can I make two cells edit and display the same information in Numbers?
You can't make 2 cells which content would be synchronised from each other.

To define b1=$a$1 and a1=$b$1 would create a loop of cross references.

This graph of dependency would be a cycle.

On the other hand you van make 2 cells depend on a common source:

a2=$a$1 and b2=$a$1.

This graph of dependency is a tree.