Actually there is a difference:

Cette lettre est à ma fille

This letter belongs to my daughter

It is her property, but we don’t know who wrote it. The sentence focuses on the owner, not the writer.

The other form can be ambiguous:

Cette lettre est celle de ma fille

It could mean both:

This letter belongs to my daughter.

This is a letter from my daughter.

However, without further information, the second meaning is the most likely.

EDIT:

Luke’s comment adds some precious information:

Cette lettre est celle de ma fille

Can also be seen as an emphasis on this letter regarding some others that could be there.
It could then be translated to:

This letter is the one that belongs to my daughter.

This letter is the one written by my daughter.

Note that “celle” is a pronoun that replaces “la lettre” and it does not indicate a possession (for instance, you could say “Cette lettre est celle que j’ai trouvée par terre”. The possession comes from the preposition “de”.

“de” can be used to indicate possession after a noun or a pronoun. In slang/familiar language you might hear “à” after a noun (ex: “La mère à Titi”, song from Renaud), but this is not regular French.

“à” can be used to indicate possession after some verbs (appartenir à quelqu’un, être à quelqu’un). Note the “être à” is more familiar/spoken French than “appartenir à.

In your example, it is not completely clear in what sense the letter belongs to “ma fille”, but I would say that

Cette lettre est celle de ma fille.

most of the case means that it was written by my daughter, while

Cette lettre est à ma fille 

always means that it was received by my daughter (otherwise, I would have said “Cette lettre est de ma fille” to indicate that it was written by my daughter.)

ATTENTION : L’exemple pris d’une lettre ne rentre pas vraiment dans le cadre général qu’exprime la question.

Dans le cas général, on se rapportera à la réponse apportée par P.Manthe.

Une lettre, au même titre qu’un livre, une composition artistique… représente le produit d’une activité intellectuelle.
Et dans ce cas précis, il ne subsiste aucune ambiguïté :

– Cette lettre est à ma fille : Cette lettre appartient à ma fille.

– Cette lettre est de ma fille : Ma fille est l’auteur de cette lettre.

A

The meanings are different; you cannot translate the first one by the sentence you propose, i.e. “This is my daughter’s letter.”

Let’s consider a concrete case; you want to tell someone that the letter you are handing them is a letter you talked about formerly and that was known to both that person and you as your daughter’s letter. There is no way to say to that person “Cette lettre est celle de ma fille.” because that does not correspond to the context. In English you can say, as you hand that person the letter “This is my daughter’s letter.” (I think that you’ll agree with that.). However, in French, you can say “Cette lettre est celle dont je vous ai parlé.”. « Celle » does not designate any more a letter written to your daughter or belonging to her and as different from other letters owned by other persons such as for instance your daughter’s friends, but a letter that you’ve talked about recently; the letter is still the same, it is still your daughter’s, but you characterise it through another of its attributes.

It is useful to see now what this first sentence means in English and and to see more precisely why the translation proposed isn’t right.

We saw that “celle” can be made to work on the condition that what follows should be made another specification. The reason it does not work with the initial specification is that when you say “celle de ma fille” you imply that there are other letters in the context and the one you specify is your daughter’s, and not anyone else’s; in doing so you refer to an idea as if it had already been talked about whereas it hasn’t; the person listening to you will find that bizarre.

There are two possibilities to render “celle” in the context of this sentence in English; they are all equivalent except for how is interpreted est celle; they are the use of the pronoun “one” and the use of the determinative definite article “the”.

This letter is the one belonging to/from/written by/sent by my daughter.
This letter is the one that belongs to/is from/has been written by/has sent my daughter.
This is the letter belonging to/from/written by/sent by to my daughter.

There are no other possibilities, no lurking ambiguities in this construction.

B

The second sentence is translated as follows;

This letter is my daughter’s.

So the proposed translation is right as applied to the second sentence only.

C There is, of course, a difference between “celle” and “à”; sometimes such differences can be made out clearly enough in the nouns those parts of speech have; in this case “celle”, “celui” and “ceux” are called “demonstrative pronoun” and that means “a word put in the place of a noun and which shows something, which points at something”. “à” is only a preposition; it stands for no noun, it points to nothing.

It should be understood that there is not one single notion involved in that first sentence: in particular not specially the notion of possession; if the question is “Who wrote the letter?” the notion is that of “agent”. In the following there is not the least idea of possession, yet the principle is the same; the idea is an idea of position, for which “à” is perfectly suited. If the position or place is characterized differently, the preposition will change, but not the pronoun.

1. Cette lettre est celle de droite. (implicitly stated precision: not any other letter)
   Cette lettre est à droite.
2. Cette lettre est celle qui était dans le pot. (that is, for example, not one of those in the wooden boxes)
   Cette lettre était dans le pot.

To add to what has already been said, this is like asking what the difference is between

This letter is that of my daughter

and

This letter is my daughter’s

for yes, there’s a similar construction in English with the anaphoric pronouns that/those.

Nos intérêts sont ceux de nos clients.

Our interests are those of our clients.

You could replace celle by la lettre:

Cette lettre est la lettre de ma fille.