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Elias, of course, is a Greek form of the Hebrew name Elijah (more properly, אֱלִיָּהוּ, Eliyahu; the Greek alphabet can’t represent a medial “h”).
Since Joseph Smith taught of a character called Elias who is distinct from the historical prophet Elijah, many critics have contended that he simply didn’t understand that Elias and Elijah, in his Bible, referred to the same person.
But it’s nowhere near that simple, as ought to be evident from the sheer fact that, in these passages, John the Baptist is described as Elijah/Elias — which, barring a totally invisible and unknown ancient Jewish/Christian doctrine of reincarnation, he most obviously wasn’t in any literal sense, and was never claimed to be.
For a helpful compendium of LDS ideas on this subject, see
http://en.fairmormon.org/Mormonism_and_temples/Elias_and_Elijah_at_the_Kirtland_Temple