There appears to be 2 legendaries on each species in the anime: a shiny and a non shiny. This is implied by the dogs appearing non shiny in some movies/episode and shiny in the Zoroark movie.
The only exception to this theory would be Lugia, if you count the baby Lugia.
The Celebi is probably the same Celebi, however, there is no evidence.
Like the Mewtwo in the first movie is the same Mewtwo that Ash encounters later on.