I think they are not on the same world but must be in the same Universe. Think about Wegner's continental drift theory. The monsters in the games are very alike. I remember the bomb monster was in many of the FFs. Also airships are in the FF's. Infact there are some similarities in the cultures of each game. Can't think of any now but I'm sure there are some. With these facts I would assume they were connected some how but seperated slowly over time. Summons most likely travel through the barriers between the planets. Bahamut Zero I think it was, was flying through space in his summon. Others like Ifrit and Shiva IMO were never really the same in each game. More like the element choose to use that form to represent them when summoned. Not sure if this is a spoiler so watch out. Cloud was brought to the FFt world so they must be connected.