This is an electronic musical instrument that can make musical sounds. It typically has numerous "patches" (sometimes called "programs" or "instruments") of sounds, often including acoustic instruments like Piano, Guitar, Woodwind and Brass instruments, Strings, etc, as well as perhaps an assortment of synthesizer sounds.
But, although a sound module can make sounds, it has no facility for a musician to directly control it. It has no built-in controller (ie, a keyboard, or a ribbon controller, or guitar fretboard, or any other device that the musician can use to trigger the sounds). A sound module has only its built-in sounds, and is therefore designed to work in conjunction with some other device that controls it.
There is no standardized terminology for describing such a musical instrument. Some people instead call it a rackmount synth (or sampler) because of the fact that many of these instruments are designed to fit inside a standard rack. Others call it an external synth (or sampler). I prefer the term "sound module", and use that term throughout my web site.
Nowadays, most sound modules are multi-timbral and offer at least the General MIDI Patch set.
Most computer sound cards nowadays have a built-in sound module to "play" MIDI messages. These built-in sound modules may employ older analog circuits such as FM synthesis, or more modern digital waveform based circuits such as wavetable synths, or even more modern hybrids such as physical modeling synths.
A drum box is a special purpose sound module that has only drum sounds in it. But, it may also have pads or buttons to trigger those sounds, in which case it can be considered to have a very limited, built-in controller.
This is an electronic musical instrument that can be directly played by a musician. It therefore has a keyboard, or ribbon controller, or guitar fretboard, or a mouthpiece (ie, as in a breath controller), or drum pads, or some other device to allow the musician to play it. It is often used to control sound modules or other MIDI devices which need to be remotely controlled.
Many controllers also have a built-in sound module, and are therefore self-contained musical instruments playable by a musician. But others have no built-in sound module (although they will typically have buttons to select patches upon a remote sound module), and therefore need to be used with other sound modules.