I'd say it depends on how you define 'lighter'. Even today, all a lighter really is is spark-maker that sets fire to something flammable...gas or wick. By that definition, even a caveman using a piece of flint to light wood-shavings was using a 'lighter'. Matches, on that basis, are much more recent, even though they too are ancient.
Definately the Lighter, it was invented by a German Dr, Dobriener or somthing. But it was not commerically viable at the time, so matches were probably available first!