Since "Fiji" sounds like "Figi", it's no wonder
people spell it that way too. The Figi Islands, however, is the same
nation as The Fiji Islands.
Although quite a bit less common than spelling it "Figi", Fiji
is also misspelled as Fidji. Adding a "d" sound to the first syllable
of Fiji doesn't seem to be consist with common spelling mistakes
however the French spell it "Fidji" so prehaps that has something
to do this it.
Of course languages other then English make many variations as
well. For instance, Spain calls The Fiji Islands, "Islas Fiyi".
Still the most common misspelling is "Figi". So when you see "Figi
Islands" or "Figi Resorts" or "Figi vacations" you can be sure they
mean "Fiji".