Vixen - missed the main problem in your original post - not a metronome does NOT count quarter notes, it counts major beats.

A reel is usually written with a 2/2 or "cut time" signature - two beats to a bar, and around 100-112 of those beats per minute. Hornpipes are a bit slower, quick marches slower still (84bpm, say).

A jig ALSO has two major beats to the bar (on eighth-notes 1 and 4) and goes a bit faster than a reel (though jigs vary enormously in speed depending on the kind of dance people are doing to them).

The only common dance with four beats in a bar is a strathspey. Often these have the same tempo as reels, so the bars are twice as long. Except when you use them as schottisches, in which case they're in 2/2 time and go at similar speed to hornpipes.

Polkas are anybody's guess. You have to know the dance. Scottish ones are more dotted, rhythmically irregular and slower than Irish ones on the whole, but there are some Irish polkas that are always played quite slowly as well. Continental polkas tend to be slower than Scottish ones.