I need to know what is the proper name for... when somebody writes ( in pencil ) in a book a short message on the inside of the cover in which they say something like: " From Smith Family to Browns! ( dated and signed ) Paula and Paul Smith". ( Somebody told me it is a "dedication" but I have a feeling it is called differently ). Thanks!

"Dedication" means that you dedicate the book , its authorization and publication itself to a person or persons. You're talking about an inscription and signature. This sounds like just a gift inscription, not even from the author, just the giver.

That is the right word. Your probably thinking of the word inscription.

Sarah