Then why’re you learning this stuff at all?

Anyway speak as you like, don’t let people get mad at you for silly reasons. However, the song/tune distinction makes etymological sense, as song is from sing “to sing”, and the use of “sing” to mean “play an instrument” is obsolete if it ever existed in English (in Latin it does, cano tibiam et cano carminem “I play the flute and sing a song”); and tune is from tone which is from Latin tonus which is from Greek tonos, which refers to a “strain” and in music means a pitch or succession of pitches regardless of device used to make them. So naturally you can’t sing something on an instrument, but you can produce a tune on any instrument, including voice.
It’s actually the same way in old hymns, at least American and German ones- this isn’t just an Irish oddity. Let me explain, and do pass over if this bores you.
In hymn jargon, a “hymn” is the words, and it is sung to a “tune”, together making a “song”. “Song” can also mean just the words, but never just the melody- those are always “tunes”.
For example, I can sing the hymn “Come Thou Fount” to NETTLETON (the usual tune) or RESTORATION #1 (usually sung to “Come Ye Sinners Poor and Needy”), and the tune PLENARY can be set to the hymn “Hark! From the tomb a doleful sound” or the song “Auld Lang Syne” (which is of course the one you’ve probably sung it to).
Of course these all can be switched up based on meter- Come Thou Fount can be sung to any 8s7s trochaic tune, and Hark! From the Tomb can be sung to any Common Time (8s6s iambic) tune. Personally, eg, I’m not the biggest fan of NEW BRITAIN, at least the way it c omes out on my voice, so I like to sing “Amazing Grace” to PLENARY. So, “hymns”/“songs” and “tunes” really are seperate entities. This was very useful in the days before powerpoint and the internet (or at least mail-order catalogs), where you couldn’t pop up any old song on your church slide projector; for variety, why not sing that old, boring hymn to another tune?
In old fashioned language, a “hymnbook” only comtained “songs” (words) with meter signs (and maybe suggestions on which tune to sing it to, given by name), and you could match any of those song to any tune that if it the meter; whereas a “tunebook” or a “hymnal” contained “songs” set to “tunes”.
A similar system used to be used in German- in the Ausbund, an old Anabaptist hymnal, the lyrics to songs, or the songs and lyrics combined, are caled “Lieder” (songs), and are “gesungen” (sung); however the raw melody a “Lied” is sung to is called the “Ton” (same word as our word “tune” or “tone”), for example you might read at the heading to a hymn “Im Ton: beim Wasserflussen Babylon” (“To the tune ‘By the Streams of Babylon’”), or “Im eigener Ton” (“To its own tune”, ie not a well-known ballad tune of the time etc.). I don’t have much experience with German hymnody so I don’t know how widespread this was (we have some Lutheran hymnals in German and English at home that use a similar system, but they’re all published in America so I don’t know if they’re using an American system), but that is indeed how it worked in the Ausbund, which is of course much older than any American hymnody.