i respectfully challenge with the answer provided by The MIDI Association. I do not believe the answer goes into the detail the question warrants as all the examples provided have severe limitations.
A controller can be used to control (as with lighting or daw controllers) or convert musical playing into midi data.
The Roland GR-55 is a synthesizer or sound module. A 13 pin (non midi standard) GK series or compatible pickup receives the musical playing. Both devices are needed to convert musical playing into midi data.
The Fishman Triple Play (http://www.fishman.com/products/series/tripleplay/
) has pickup, convertor and data transmitter in one device but the wireless receiver has a USB footprint and requires a computer to operate,
The AC-Pad has controls but can not convert musical playing into midi data.
Casio and Yamaha made several guitar styled product lines that combined pickup, convertor and sound module into the guitar (or guitar like) body. None are currently in production.
Here's a pretty good overview https://en.wikipedia.org/wiki/Guitar_synthesizer#Guitar-based_models
Inspired Instruments, Inc. came out with the YouRock midi guitar controller in 2010 and updated it in 2013. It can be used as a game controller or as a midi guitar controller. Here's more about it and the Lineage midi guitar recently added. http://www.yourockguitar.com/21555-2/