Hey,
Wow, a lot more answers than I expected!
Here is a REALLY simplified definition of the three:
Acoustic - describing an instrument that doesn't need electricity or electronics to generate its sounds. Example: a drum kit, saxaphone, piano.
Analogue - describing an instrument that does need electricity and electronics to generate its sounds. Example: an old synthesizer from the 70's.
Digital - describing an instrument that needs a computer chip or other integrated circuit to generate its sounds. Example: a sampler.
I stress that this is an oversimplification, please don't bombard me with contradictions...
So, if someone wanted to have a bass sound on one of their tracks, you could choose between one of three different basses: an acoustic bass (like the big wooden stand-up ones used in old jazz music), an analogue bass (like the ones used in old 70's funk), or digital bass (pretty much any synth bass from 1983+).
When you use an analogue synth, you are in essence generating the sounds from scratch by telling these little electonic components called
oscillators to create a voltage and send them to your speakers. When you use a digital synth, your sounds are already pre-stored on a chip somewhere (in RAM on a sampler, in ROM on a device like the Triton). The sounds are not being generate from scratch; rather, they are being 'read' from memory.
With this is mind, it is completely possible to sample the sounds of an analogue synth, store them in RAM/ROM on a digital synth, and use them for later. When you play them back from the digital synth, they should in theory sound just like the analogue synth that made them.
So far we've only talked about digital synths as ones which store digitized representations of acoustic and analogue sounds. However, digital synths can also create new sounds from scratch as well! As a matter of fact, anyone who is able to read this post has a digital synthesizer right in front of them...a computer is, in essence, capable of doing anything that any digital synth or sampler is capable of doing.
If you have a wave editor like Cool Edit or Sound Forge (pc) or Peak or Spark (Mac), you can make cool sounds on your computer using their waveform generators. You can make the basic waveform shapes (like sine, sawtooth, triangle, square), noise (like pink, brown, white), and if you're clever enough you can make more complex waveforms by modulating one with another. Sound Forge is especially good for this, they have a simple FM synth which allows you to make sounds that were so common in the 80's.
Take care,
Nick