Tracks and channels
Tracks and channels are almost, but not quite, the same thing.
In recorded media such as magnetic tapes, you can usually record several different waveforms at the same time (even if it's just a stereo pair), which are magnetised onto several parallel lines, one each. Much like with trains, each separate line you can move along is called a track.
In live use, such as mixers (both mixer modules and mixing desks), you can mix together several different waveforms. Much like with broadcast radio that lets you tune into one particular waveform at a time, each separate input you can listen to is called a channel.
In order to hear, let alone mix down, the music recorded on a multitrack recorder, you have to connect its outputs to a mixing desk's inputs. This is a classic studio setup, and likely where the confusion between the two terms comes from. As each recorded track corresponds to a mixer channel, the terms can be used interchangeably.
MIDI continues this trend with the terminology: when you transmit a MIDI event live, you transmit it to one of its sixteen available channels, with the assumption that you own up to sixteen devices, each one listening in on one or more separate channels (generally for one timbre per channel), as well as listening to global events like the clock.
When it comes to MIDI sequencers, and how they record rather than transmit these events, they usually group them together so that each part is recorded onto a separate track that can be muted or soloed, just like on a multitrack recorder. By convention, each MIDI track tends to output to only one MIDI channel, though that's not required by the specification.
Each track can record multiple channels' events, which seems only really useful when running out of tracks in older sequencers. Multiple tracks can record events for the same channel, which is especially useful for layering up drums one at a time.
Outside the studio
House music is often instrumental, so most of it can't properly be called songs. Needing a universal term to call each single piece of music that may or may not contain singing, people started calling them tracks, as some house music contained "little more than a drum track". The term caught on, and was adopted even outside of house music.
Similarly, the optical or magnetic waveforms recorded on a movie film reel are its sound tracks, with the phrase soundtrack evolving to mean a film's music, as sold on its own as an album.
In summary: if it's a recording, it's probably a track. If it's live, it's probably a channel.
- Energy Flash Simon Reynolds, 1998, ISBN 0-330-35056-0