Reels and Hornpipes have the same number of beats in a bar. The rhytm is differen however. In general a reel has all 8 notes in constant tempo, whereas a hornpipe consists of a slightly longer note followed by a shorter one.
Hornpipes used to be written as "dotted" notes, but these days tend to be written without the dots, and so look the same as the notation for a reel. I think of a hornpipe having a rhythm which goes Dum-di-dum-di-dum-di-dum-di with the "dum" slightly longer and with a heavier emphasis than the "di".

The emphasis for hornpipes and reels tends to depend in part on the tune itself and in part on the speed it is being played. For reels, they are often played with two strong beats to the bar (beats 1 and 5 with notes in two groups of 4). With hornpipes you often find a stonger beat at notes and 5, but you also find a "lift" on beats 3 and 7. I can't think how to describe it, but it is definitely there.
I hope some of this helps.
Quack
GtD.