There are various tpyes of jigs:

Single jigs are written in 6/8 time and sometimes 12/8 time.
Double jigs are written in 6/8 time. Slip jigs are written in 9/8 time.

I have seen reference to strathpeys being written in 4/4 and 4/8 time.

Reels and hornpipes are in 4/4 time.

Much of distinction between the tune types concerns the accenting of the notes and it is not always that clear which is which (some players play hornpipes fast and flat for example - more reel like). having said that, I believe that the best way to understand the different types of tunes is to listen to examples of each and develop a feel for the tunes - same goes for learning to play them.

Favourite reel - Silver Spire.

Jon