Basically, an acoustic electric or elctric acoustic is an acoustic guitar with a built-in pickup and EQ.
A semi-electric or the more commonly used term of semi-hollow or archtop refers to a hollowed-out electric guitar. There is usually some opening in the body of the guitar, in the shape of a f-hole (two of them). These guitars are commonly used in jazz or blues music although it is starting to get popular in rock music as well.
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