Term for dedicating a book
Let's say:
John Doe writes a book -- Me and My Dog Spot. On the page after the title, he writes: For Nancy.
My aunt gives this book to me for my birthday, and on the title page, she adds in her penmanship: Dear Jen, this reminds me of you and Fluffy. Love, Aunt Marge
I'd refer to #1 and #2 as a dedication, but are there more appropriate terms?
The printed, authorial kind is definitely a dedication, as you say.
The handwritten personal kind, I would usually call an inscription, though I’ve also heard dedication. See e.g. this flickr group for confirmation of this usage of inscription.
I've heard and seen dedication used for both. The handwritten kind can be called inscription, as others have said, or an autograph (though this is more used when carrying a signature, possible of someone well-known).
Inscription is the word I was looking for regarding #2