"Acoustic" as a descriptor for instruments is a retronym (like "analog" for a watch) that came into widespread use only once electric and electronic instruments were invented. It means an instrument that is designed to be played without any electricity involved --so in other words, at one time all instruments were acoustic.
"Unplugged" is a bit different, in as much as it means taking music that was originally composed or played on electric and electronic instruments, and replicating it with all acoustic instruments. The term was popularized by the popular MTV series of the same title, featuring famous rock musicians playing all acoustic sets featuring their own work. The concept was a bit of a backlash against the heavily produced electronica of the 80's and early 90's, as well as serving as proof that famous musicians could sound good even without studio magic. The Unplugged series yielded several notable hits, including Eric Clapton's bluesy "Layla", Mariah Carey's (cover of) "I'll Be There", and Nirvana's "All Apologies."
All "unplugged" music is acoustic, by definition, but not all acoustic music is "unplugged." Classical music, for instance, is acoustic, but not unplugged. "Acoustic" is more of a neutral modifier, it's purely descriptive. "Unplugged," on the other hand, is more of a marketing term, it has deliberate connotations of authenticity, and carries implications of genre.