I've seen a song defined as:
A short poem or other set of words set to music or meant to be sung.
And a track as
A recording of one song or piece of music
A song clearly has connotations of singing and a track in my mind has connotations of a stored, recorded piece of music, not the abstract entity itself. In the context of an electronic piece of music with no singing, what is the appropriate term to use to refer to said piece of music?
Since a song contains lyrics to be sung it is not a song. Considered on its own, it's an instrumental, a "musical composition or recording without lyrics, or singing." For example the (electronic) instrumental "Chariots of Fire" composed by Vangelis for the film score of the same name. It's the first track on the album. A track is a section of an album, usually compromising a single song or instrumental. So as part of an album it's a track, indeed an instrumental track.
A serious piece of electronic music should be referred to as a composition, because that's where the creative work was performed.
However, if in doubt, use the term preferred by the composer. For example, Jean Michel Jarre, an early figure in electronic music, frequently uses the term concert, since he performs live and records the performances. However, on his website you will also find terms like single and album, which reflect how he saw the work being listened to.
I realize semantically music theory professors might refer to all songs as music pieces, but if they're not sung are they songs? and if they're never composed but random, are they compositions? and if they're never recorded are they tracks? and if it's not written is it a piece? So technically:
In recording, "laying down a track," means recording a song. It comes from original recording methods.
In digital audio composition, a.k.a. Electronic Music, tracks can be either:
Often these together form a composition which can be exported as a recorded file from the recording software. Electronic music can also be recorded directly to either an analog or digital recording device, making a song (think Pink Floyd pre-computer recording).
Grooved Recordings
On vinyl records and wax cylinders, tracks are physical grooves of recorded sound vibrations, all recorded at the same time. Sometimes they were songs, sung by a singer, and sometimes they were speeches. When the track ends, there's a flat spot, and then next track encountered is the next recording. This is where phrases like "cutting a track" and "laying down a track" come from since the cutting needle strikes and actually cuts a physical track or groove in the recording media when the needle is laid down on the cutting surface and power is applied to disc. It spins at a set speed, and the needle vibrates based on the mechanical input. To hear something similar to the original, play it back at the same speed and the needle vibrates in reverse as it follows its track.
Analog Audio Tape
On 8-track cassettes, the word track refers to a recording track or sample, just like audio composition, so there were sometimes 4 stereo tracks with different elements on them (drums, singer, guitar lead, bass) or they could have 8 different mono tracks. You might hear a guitar in your left ear, and a singer in your right. These could have electronic music on them as some bands experimented with analog electronic synthesizers when these were popular.
Optical Formats
Compact discs and other optical media have tracks similar to vinyl records in that they have physical "tracks" with pits and bumps that either scatter or reflect a laser light back into a lens. Rather than having physical contact with the disc, a photocell detects the laser and translates the binary data (light, no light) into sound waves or stored data files depending on the reader. Between these tracks there is a space that scatters the laser, and the laser head continues until it hits another track (or the outside of the disc). Tracks on audio cds are synonymous with songs if the audio cd contains music.
Digital Music
When people started "ripping," or converting CD music to MP3 and other audio file formats, they picked up the phrasing. So some people would refer to a song as a track, especially if they're selling analog to digital recordings. Not too many 1920s digital recordings out there that went straight to digital.
Technically speaking, song comes from the act of singing, so if it's electronic music without singing, is it really a song? Now if a synthesized voice is used, then it could sound like singing, and then could technically qualify as a song.
English is funny, especially American English, and as different cultures merged, people colloquially mix the meanings of the phrases. Spoken word might also be considered a song if it makes you think and is voiced over music.
Update Clare actually read your question thoroughly and noticed the bit about with no singing and added instrumental to her answer which is what you would call it.
It was mentioned before that you should use the composer's preferred term. This is correct but if you have no direct connection with the composer to ask this, the word track actually fits the bill quite nicely.
When composing electronic music, usually by way of utilizing synthesizers and/or a DAW (Digital Audio Workstation, what sequencing software tends to be called when it also integrates audio recording and mixing capabilities into one package), the individual samples and sequences that make up the piece are arranged into audio tracks on a mixer. Incidentally, when the work is completed and the tracks are mixed together to output a complete work, the result is a track as well. Why is this? Well...
If the end result is to create a (popular) electronic work, oftentimes this work will be taken to a stage where it will be played. In order for the work to be played, it will become a track on DJ software, or on a vinyl for a turntable. These tracks are then interwoven to create a set.
When this is not the case (for example, ambient works might not be mixed by a DJ), the word you can use in this case would be a piece or composition. This is particularly true of a "serious" work that is rendered electronically but was originally composed with a specific instrumentation in mind, or is a piece derived from a piece composed for a classical ensemble.
The moment that lyrics and singing are introduced, it becomes a song.
A track refers to a physical groove on a vinyl record, though of course it is now wider than that so both a song and a instrumental piece can be a 'track' but an instrumental isn't a song.
