"instrument for giving a graphic representation of speech," 1879, from Greek logos (see logos) + -graph "instrument for recording; something written." Earliest use (1797) is in the sense "logogriph," and it frequently was used in this sense.
"sign or character representing a word," 1840, from Greek logos (see logos) + -gram. Generically, "any symbol representing graphically a product, idea, etc." is from 1966. The earliest use of the word (1820) is in the sense "logograph," but OED explains this as a substitute "for logograph, which in this sense is itself a mistake for logogriph."