It seems to me it's a combination of tempo and rhythm. You can turn a reel or a rant into a hornpipe by slowing it down a bit and "dotting" the quavers. Roxburgh Castle is another which seems to be played differently by different people. In the folkworks session collection it's classed as a rant and is in a set with Morpeth Rant. Others play it as a reel and yet others as a Hornpipe. At Folkworks summer school I heard one of the Youth Summer School Bands play Soldiers Joy as a hornpipe.

I must admit I am not sure what makes a tune a rant, but listening to some recordings it does seem there is a little more emphasis on the beat than a reel and a hint of lilt in the quavers.

I was playing around with a tune some while back (I can't remember which now) and I found that by slowing it down, dotting the quavers and adding a snap or two I could turn it into a Schottische or Strathspey.

This leads me to the conclusion that what form a tune takes is a based on what people say it is (custom and practice or expectations) and how you play it.