Lately, I’ve been wondering a few things…
What makes a jig, a jig?
What makes a slip jig, a slip jig?
What makes a double jig, a double jig?
How are these three different from one another?
What makes a reel, a reel?
And what makes a hornpipe, a hornpipe?
What are these two different?
I guess I just have a hard time telling the difference while just listening to them.
That was just the page I was going to recommend. I was listening to a CD today that I have listened to quite a few times but not really learning about the tunes. I quizzed myself each time a new set came on and I did miserably—I won’t even tell you what I mistook for what, we are talking miles apart 
. I was pretty bummed out because I thought I was improving. That being said, I truly believe that one can get better at listening, but it just takes time. The first step is learning about the types. So good for you. And then listening a lot.
http://www.slowplayers.org/SCTLS/learn.html
This page is about learning by ear but it also talks about the structure of tunes. You might already know everything there, but it was a helpful explanation for me when I started listening more carefully.
Primarily, the type of dance steps used to dance to the tune, and the rhythm of the tune, that matches or compliments the rhythm of the dancing feet.
Unfortunately most people who play never get to play for dances, and don’t get to enjoy the feeling that results from seeing people dancing to their playing.
Jig:
Jesus and mary and jesus and mary and :||
Slip jig:
Jesus and mary and joseph and jesus and mary and joseph and :||
Double jig:
Jesus and mary and holy St. Joseph and :||
Reel:
Watermelon watermelon :||
Mazurka: “plenary indulgence, plenary indulgence”.
Marvellous. 
Hop jig:
Buy the band a beer, Buy the band a G&T :||
Careful there fidd…
Somebody’s liable mistake ya for one of those musicians
that sit around all night dinners after bar close,
(hopin’ that the inattentive waitress will bring ya a 3rd cup,
when ya both know ya don’t have the cash for a tip)
thinkin’ up pneumonics,
and arguing which is better for a certain tune!
lol - nah - I just ripped them off the lovely folks at thesession.org.
more that a passing similarity there…
reminds me of a saying about programmers and musicians.
“Good programmers don’t borrow, they steal.”
come to think of it the programmer that said that played bass…