Marion
You can basically play almost any tune you want in the rhythym/tempo of whatever dance you are doing.
For example there is a hornpipe called "Soldier's Joy" which we always play as a reel.. just to give it some guts..
As far as jigs are concerned there are single, double, treble, slip and slides.. all depends on how many steps you are expected to make in any given bar... and agin almost any tune can be "converted" to suit..
There is a tune called " Visit To Ireland" which is deemed to be a treble jig.. i.e. if we played it for the dancers it would be quite slow due to as Radriano said the dancer having to get more steps in.. though if we play it simply as a tune it usualy gets done at double jig tempo...
Likewise for "St. Patrick's Day".. a tune composed for a treble jig, though more often than not performed by ceili bands as a "normal" jig.
Hornpipes tend to get the same treatment as well, which I personally don't like.. played fast they tend to loose all the bounce which makes them a favourite of mine.
And then there's the perenial favourite of bands of crossing over reels and polkas. I've even heard slides played as polkas
No doubt this has confused you more than helped
Cheers
Mick