The way I think of triplet vs. treblet, for what it's worth:
Triplets:
Triplets are always part of the tune as written/composed. If there is sheet music for the tune, they'll be written down in the sheet music. Everyone in an Irish session will be playing them the same way, in the same place in the tune.
Triplets follow the tempo of the tune. You can hear this in tunes that include triplet phrases like "Brenda Stubbert's Reel," where the triplets that begin each phrase will be faster or slower depending on how fast Brenda's is being played.
Treble Ornaments:
Trebles are an optional series of notes played as personal expression, and may be inserted (or not) at different parts of the tune by different musicians. Although, there are some conventions where trebles are more likely to be used. Like whenever there's a lone quarter note in a jig that cries out to be "trebled." Trebles are never written down in sheet music, unless it's part of a tutorial on ornaments.
In common with other Irish ornaments like cuts and rolls, the speed of a treble ornament is usually independent of the tune's tempo. It's a quick burst of notes from the flatpick, regardless of how fast or slow the underlying tune is being played. A treble might also be played "percussively" where you don't hear much of any actual pitch in the note. I think this is more common with tenor banjo than mandolin, due to the single vs. double-course strings, but there is still some room to decide how much pitch you want heard with the pick attack.
There may be other subtle differences, like whether the notes within a treble are pitched differently or not, but that's how I think of the differences.
Edit to add: Oh, I just thought of one other difference! You can screw up a treble ornament by not hitting it quite right (which I do frequently), and as long as you're still maintaining the rhythm of the tune, nobody cares. If you screw up a triplet, then you've screwed up the actual tune. And someone will probably notice.
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