I think they originally called themselves the Islamic State of Iraq and Lebanon, hence the prevoius acronym ISIL. Now it seems to be Iraq and Syria they are concentrating on hence ISIS.

Either way they are not a legitimate state and quite rightly shouldn't be recognised as such as that would tend to give them credence or a kind of twisted legitimacy.

Don't quote me on this, perhaps ISIL and ISIS are completely different entities, either way they are terrorists nothing more.