The simplest answer to the original question is the rhythms, as discussed above. Obviously, there is more to playing music than to counting notes. Foolestroupe, I like your description of the guy in the Mall who just kept playing notes one after the other until he ran out of breath. He is a teacher's nightmare. The "feel" of jigs, reels, and hornpipes comes from their respective dances, but there are other considerations. When playing concert style, the rhythm and the ornaments can be quite different from those played in dance style. For concert (not necessarily a "real concert," but listening instead of dancing), instrumentalists can take a lot of liberties with rhythm that we wouldn't dare do for dancers. For dancing, you have to play the beats steadily and somewhat emphatically, but you can take liberties in between the beats. If the dancers are up in the air, you've got to bring them down to the floor at the right time. You can make some subtle changes, though. When I see and hear a really good fiddler (like Steve Hickman) playing for a dance, I can face him, keep my back to the dancers, and still know what the dancers are doing differently according to the way the fiddler is playing. When the fiddler plays smooth, connected notes (often slurred, dotted slurred, or legato), the dancers glide more. When the fiddler plays with little hesitations (staccato, dotted slurs) between the notes, the dancers use a bouncier step. (This is hard to describe in words. It's much better to listen and watch.)

Likewise, the strathspey is best understood by listening to the music than by reading descriptive words. In Celtic music, two consecutive eighth notes are generally not played for the same length of time. One or the other can be a little shorter, then the next one a little longer, but they still add up to one beat. Exaggerate the rhythm a bit, and you have a dotted eight note followed (or proceeded) by a sixteenth note. Play the dotted rhythm for two consecutive pairs of notes, and that's a strathspey. The dance movement for a strathspey is smooth and gliding, and that's how the music is played. There are some subtle matters of style, of course. Strathspeys can be played in dance style or concert style.

These are some of the tings that make playing music so much fun, the Mall musician notwithstanding. If you just play one note after another, all with mathematical precision, that's noteplaying, not musicmaking. Music making is fun.