Scottish, Irish, and just generally Gaelic Flute Music?

[OC Richard]

The terms "reel" and "jig" seem to correspond between both the traditional Irish flute playing and the Scottish country dances...

You're correct, both Scottish and Irish dance music have both reels and jigs, and they're often played pretty much the same in both traditions.

Scottish "country dancing" and Irish "ceili dancing" are similar in many ways, though the specifics of the footwork are different. (Ceili is also often spelled ceilidh, the final "dh" is silent.)

Irish ceili dancing https://www.youtube.com/watch?v=_HhC_4jPigc

Scottish country dancing https://www.youtube.com/watch?v=EqShm5XeKMA

There are cases where reels or jigs can sound rather different in Irish and Scottish music, two examples are

1) in Irish "step dancing" they have "heavy jigs" which are played much slower than jigs normally are https://www.youtube.com/watch?v=fcfD4PQwD2E

2) in Highland pipe music reels are generally played "dot/cut" or "pointed" and also often somewhat slower than they would be for either Scottish country dancing or Irish ceili dancing. A lot of Highland pipers used to heavily "point" jigs as well though this isn't in fashion as much nowadays.

Highland pipe March, Strathspey, and Reel, jump to 2:59 to hear the reel played at 86bpm, far too slow for RSCDS or ceili dancing
https://www.youtube.com/watch?v=iWdIn38-5xM

(I should mention that in Scottish Country Dancing no distinction is made between reels and jigs, both are called "quick time" and you do the same steps at the same speed for both.)

what did you mean by 'on the stream'?

On Irish flute some players have a lot of rhythm, a lot of pulsing, in their blowing while others play with more even blowing, which you'll sometimes hear called "playing on the stream" or playing with "flow".

Are there specific musical traits that uilleann pipe ornaments draw on?

There's quite a catalogue of ornaments that uilleann pipers draw on. Sometimes uilleann pipe music is very heavily ornamented, more so than players of other Irish traditional dance instruments (flute, whistle, fiddle, box, banjo) would deem suitable.

However since the finger-holes and fingering of the whistle and flute aren't that much different than the uilleann pipes there's a certain amount of shared technique between all three instruments.

So uilleann pipes, Irish trad flute, and Irish trad whistle all generally play cuts, pats, and rolls in more or less the same way using more or less the same fingerings.

Though using different fingerings, cuts and rolls can be played on fiddle too, and are often heard with Irish fiddlers.

Irish box-players and banjo-players have figured out ways to play analogous ornaments on their instruments as well.

Other uilleann pipe ornaments, though generally viewed as being more uilleann-specific, are sometimes played on whistle and flute, for example the "crans" that you can hear Matt Molloy playing on Bottom D.

Then there are other ornaments that are uilleann pipe-specific like Hard Bottom D, Ghost D, "tight" triplets, backstitching, barking, etc.