Acoustic Guitar – with under saddle pickup
This is the author’s guitar, a Lowden F32C. It’s is a normal acoustic guitar but I have been able to use it at gigs, amplified, because it is fitted with an undersaddle piezo pickup. 
An acoustic-electric guitar is just that, a normal acoustic guitar with an added method of amplification using a pickup of some form or another.
Piezo electric pickups have been around since the 1970s and Ovation, with their bowl shaped backs, were were one of the first guitars to have them fitted. The pickup comprises a strip of material that reacts to vibrations and produces an electric current as it does so. This method of amplifying the guitar is quite advantages when an acoustic guitar is required in many performance sitiations. Alternatively using a microphone, unless in a studio environment, can prove tricky. Unlike a oicrophone, the piezo pickup will not course feedback. (Though the resonance of the guitar body may still cause the problem with feedback)
One disadvantage of the piezo pickup is that, when fitted to an acoustic guitar, the sound you are hearing is not actually of the guitar’s natural resonance that pushes air through the sound hole. Instead it is a faithful correlation to the way the strings are vibrating. Careful tonal control will be required in the method of amplification.
On the socket panel above there is also a facility to plug the guitar directly into a computer for recording.
An alternative to an under saddle pickup is a sound hole pickup.