It's the method of atomization.

Flame: You spray a (usually aqueos) solution into a (usually C2H2/N2O-air) flame, which produces the energy to vaporize the solvent and to produce atoms of the element desired. N2O-air gives higher temperatures than C2N2-air. Advandage: inexpensive, fast; Disadvantage: interferences related with all chemical reactions in a flame. Concentration range: typically mg/L; ppm.

Graphite furnace: No flame. Atomization ist performed within a graphite tube. Graphite is electrically conductive and heats when passing electrical current through it. To prevent burning of graphite, a shielding gas (typically Ar) needs to be used. Advantage: No flame interferencees; Disadvantages: Slow, fomation of carbides, atomization depends on element compounds ("chemical modifiers" are used to minimize all that); Concentration range: typically µg/L, ppb.

Hydride: For elements that form volatile hydrides (As, Se, Hg, Sn). You bring your (normally acidified aqueos) solution into reaction with NaBH4 or SnCl2 solution, where the nascent H forms volatile hydrides which are seperated as gas (in an Ar flow) from the matrix and are transferred into the spectrometer, where they dissociate in a heated cuvette. Advandages: Best possible matrix removal; Disadvantages: time-consuming, sensitivity may depend on species (As3+ is ways more sensitive than As5+), which may require additional steps of sample treatment. Concentration range: typically µg/L, ppb.

Thank you Thomas Fischer

Method of atomization - please refer to any book about atomic absorption analysis, there is a lot of them.

Briefly: flame is cheaper, quicker, but lacks of sensitivity, also for some elements hotter acetylene - nitrous oxide flame is required. Please forget about propane-butane flames as they are known for interelement interferences. Furnace gives your the best detection limits, but is slow, expensive, useless for carbide-forming elements (such as tungsten) and has a lot of matrix effects for volatile elements (cadmium, lead, arsenic etc). I believe it is the most capricious method from all I know.

Hydride generation is good for especially mercury, selenium, arsenic. I've heard about applications for antimony, lead and tellurium but never seen in real life. Anyway this method is linked with chemical reaction and it leads to complicated sample preparation and also to masking of some elements those caused interferences - copper, iron etc. The method is almost always cannot be used for complicated matrices such as metals and alloys.