Here's one more data point for the single jig discussion:
Matt Cranitch in his book "The Irish Fiddle Book: The Art of Traditional
Fiddle Playing" (Mercier Press, Cork & Dublin, 1988) says
"...slides, strictly speaking, are single jigs...The word 'Slide' derives
from a sliding movement of the dancers. Through usage, it has come to
means them;usic that is played, as well as the dance itself. The term
'single jig' is rarely used now in this context.
"In the slide, the duration of the beat is a dotted crotchet, as in the
jig (here he's referring to the double jig). However, the note-pattern
for each beat is mainly crotchet and quaver, and to a lesser extent,
three quavers, whereas in the jig, as we have already seen, the revese is
very much the case. This gives the slide a very different and distinctive
feeling: it has a great 'swing', which can be heard in a Duggan's Slide.
The time signature is 12/8 with four beats in the bar."
Slides for which music is given in the book are
The Brosna Slide
The Cuil Aodha Slide
Dan O'Keefe's Slide
Denis Murphy's Slideds (Nos. 1 and 2)
The Gloutane Slide
Johnny Murphy's Slide
Mick Duggan's Slide
Nell O'Sullivan's Slide
Padraig O'Keefe's Slide
The Scartaglen Slide
The Toormore Slide
Danny Ab's Slide
Finally, my daughter does step dancing, and they do single jigs but have
never heard of a slide.