I'm noticing a slight trend toward calling anything hardware "outboard". Like you have software synths and you have "outboard" synths. I prefer to refer to hardware synths and synth modules by just that term "hardware". Before soft synths that wasn't necessary.
I think the term "outboard" goes a lot further back though when you are referring to signal processing devices like hardware eq's, compressors, fx, etc.
We also need to distinguish between midi signals and audio signals. Most synths don't process external audio, although some do. In fact, most synths don't process midi information either, they simply respond to it. Big difference between that and audio signal processing gear in the traditional sense.