LEF file contains library information for a class of designs. Library data includes layer, via, placement site type, and macro cell definitions. You can define all of your library information in a single LEF file. However this creates a large file that can be complex and hard to manage.
LAFF is the file format generated by TI. It is the extracted view of the layout.
Laff has all the layers description, the layout objects and their co-ordinates hierarchy wise. From the laff file, the layout can be generated.