Interesting question. I've copied some information on it below. In summary, the two species are very similar, the main way to separate them is by geographic area since they don't really overlap except in western Indonesia, and scientists can't tell if they're distinct species or two populations of a single species.
http://www.fishbase.org/Summary/speciesSum...esname=volitans
Pacific Ocean: Cocos-Keeling Islands and Western Australia (Ref. 27362) in the eastern Indian Ocean to the Marquesas and Oeno (Pitcairn group), north to southern Japan and southern Korea, south to Lord Howe Island, northern New Zealand, and the Austral Islands. Replaced by the very similar Pterois miles from the Red Sea to Sumatra
http://www.flmnh.ufl.edu/fish/Gallery/Desc.../RLionfish.html
The genus Pterois contains eight species variously referred to as lionfishes, turkeyfishes, or firefishes. Relative to its seven congeners, Pterois volitans is diagnosed largely by differences in number of fin spines or rays, coloration, and scale type. Although not definitive, the presence of spots on the dorsal, anal, and caudal fins as well as the size of these spots (larger in the red lionfish than in the most closely related species) is useful in making a preliminary distinction between P. volitans and other lionfishes.
http://nas.er.usgs.gov/queries/FactSheet.asp?speciesID=963
The devil firefish (Pterois miles) is closely related to the lionfish (P. volitans). In fact, P. miles and P. volitans have been treated as the same species (i.e., as synonyms) as well as distinct species (Schultz 1986). The devil firefish is found primarily in Indian Ocean and Red Sea, but has also migrated through the Suez Canal to the Mediterranean Sea (Golani and Sonin 1992). The two species co-occur in western Indonesia. Although it appears very similar to the lionfish, the devil lionfish has fewer dorsal- and anal-fin rays (see Identification, above). Recent genetic work (using mitochondrial DNA) was unable to reveal whether P. miles and P. volitans are distinct species or two populations of a single species (Kochzius et al. 2003).