Question: How do the Catholic and the Orthodox Churches differentiate between which Apocrypha are part of their holy tradition and which are not?

For example, the story of the Presentation of the Blessed Virgin Mary is not contained in any books of the Bible and is rather coming from the early Apocrypha: "The Protevangelium of James". 

However, as far as I know, at least in the Orthodox Church this story is absolutely believed upon and its validity is never questioned. The Orthodox definitely consider this story to be a part of their tradition. On the other hand, there are many Apocrypha that describe exactly the same stories that are described in the New Testaments, however, those Apocrypha are just considered Apocrypha, their authorship and spiritual validity are held under question, and they are not considered by the Orthodox to be the part of their tradition.

Answer: 
There's the Gospels of Eve, Judas, Philip, Mary, Ebionites, Hebrews, Marcion, Mani, Apelles, Bartholomew... there's a huge list. To be "Apocrypha", a book need only be unaccepted into the official Bible. This, added to the propensity of early Christians (especially Gnostics) to write what were essentially fan-fics at the time, and you end up with numerous [apocryphal books.](http://en.wikipedia.org/wiki/New_Testament_apocrypha)

Different denominations' canons can be found [here](http://en.wikipedia.org/wiki/Books_of_the_Bible) under Intertestamental books and [here](http://en.wikipedia.org/wiki/Biblical_canon).

As for why some are canon an some are not, for Catholics it was decided in the [Council of Trent](http://en.wikipedia.org/wiki/Council_of_Trent) and subsequent discussions, while the [Eastern Orthodox canon](http://www.catholicbridge.com/catholic/orthodox/why_orthodox_bible_is_different_from_catholic.php) is still mercurial, for a lack of such a unified council.
I'm not aware of any. I would say that it's not possible. First off, there is no single Bible. The word "bible" means "books" plural in Greek. Various groups picked certain ancient books to be part of their Bible, and ignored many others. Different groups ignored different books. The Protestant believe there are 66 books. The Ethiopian Orthodox Church says 81. Some churches regard "Book of Jubilees" to be holy, and other don't. Each church decided which books were going into their bible, and if they didn't, the book is not holy to them by definition.