My vague memory from my Irish dance classes 15 years ago was that the "treble" referred to putting in 3 beats or taps per beat of music; a corruption of triple, perhaps. In order for it to be humanly possible for the dancer to add these "grace" notes or beats, the jig has to be slowed down, but is still the same basic 6/8 rhythm.

In soft shoes, the step is the (hop, hop back, hop 1,2,3), again to 6/8, but can be done to a faster tempo because there are fewer taps or steps per beat. I have heard these referred to as "double" jigs, and don't know what a "single" jig might be.

I never did learn to slip jig - I never got the weird combination of 7+2 to make 9/8, but I love the sound of slip jigs like "Kid on the Mountain".