I believe that SE has stated that 'officially,' the worlds are entirely separated. The races looking similar with similar backgrounds was apparently only done to be friendly to those XI players going to XIV.
... this is not to say, however, that this will stay this way. In fact I think it is very possible that the two may be linked, although perhaps it is not the same world but an alternate timeline/dimension. Adventurers of Vana'diel are well versed in multiple dimensions... dynamis, promyvions, the new "parallel" world to Vana'diel, Abyssea, and also time travel and a whole separate timeline. To consider the possibility that there is yet another world, would not be too far fetched in XI's terms (we have yet to see multiple dimensions in Eorzea).
I am definitely curious about something shantotto says though in XI, after she travels and visits "another world very similar to Vana'diel." People have suggested it to explain her appearance in Dissidia, but I think it could also explain Abyssea, and a possible link to Eorzea if one is there. Time will tell.
... this is not to say, however, that this will stay this way. In fact I think it is very possible that the two may be linked, although perhaps it is not the same world but an alternate timeline/dimension. Adventurers of Vana'diel are well versed in multiple dimensions... dynamis, promyvions, the new "parallel" world to Vana'diel, Abyssea, and also time travel and a whole separate timeline. To consider the possibility that there is yet another world, would not be too far fetched in XI's terms (we have yet to see multiple dimensions in Eorzea).
I am definitely curious about something shantotto says though in XI, after she travels and visits "another world very similar to Vana'diel." People have suggested it to explain her appearance in Dissidia, but I think it could also explain Abyssea, and a possible link to Eorzea if one is there. Time will tell.