I’m a kid of the 80’s. I pretty much grew up with Daisy Duke’s, so I am all knowing and my mastery of vocabulary is unfalable 
Referring to the pick of Mary Ann from Gilligan’s Island up thread:
http://www.babble.com/CS/blogs/homework/mary-ann.jpg
I can’t tell what fabric is used in that pic, but even if it is denim, I would consider it more of a hot pant with the high waistline and hemmed cuffs around the leg. Kind of what Linda Carter wore in Wonder Woman:
http://img.villagephotos.com/p/2006-1/1134258/Wonder%20Woman%20-%20Color%20-%20001.jpg
Hot pants have been updated lately though. I would consider these hot pants as well despite the lower waistband. They are kinda tight and stretchy:
http://www.mmmmhot.com.au/sites/mmmmhotcom/assets/public/image/products/featured/415/690x570/hot-pants-690-2008-06-19-11-06-54.jpg
Daisy Dukes are cutoffs, but they are a specific subset of cut-offs. These are cut offs, they still have some of the pant leg remaining:
http://www.kaboodle.com/hi/img/c/0/0/4c/f/AAAADArKmDgAAAAAAEz3Rg.jpg?v=1242761894000
Here is a picture of Daisy Duke herself:
Notice the waistband is much lower than the hot pants of the day (see Wonder Woman) revealing her bellybutton. They are obviously jeans at one point, in that the pockets are “jean-like” compared to Mary Ann’s pockets. Also, the hot pants pretty much covered the butt cheek and we can see a bit of butt cheek in Daisy’s photo. Just like the cutoffs, Daisy Dukes have the frayed hem.
I would say that to most people, Daisy Dukes are a low rise denim jean that had the legs cut off even with or above the crotch seam.
The Bermuda shorts are usually shorts that are of a much nicer quality that supposed to be more formal usually ending just above the knee.
For men:
And for women:
Just regular jean shorts are different than cut offs. They are very much like a Bermuda short but they are made of denim with a stitched cuff:
The jean short has developed a slang term, “jort” a combination of the words jean and short, but is becoming increasingly applied to ugly cutoffs and Daisy Dukes. If someone complements you on your jorts, you are probably being made fun of.
In all of the pictures that I could find of Daisy Mae Scragg, I can’t tell if she is supposed to be wearing Daisy Dukes or a tight, short skirt that has been frayed.
Finally I went looking to see what Ellie Mae wore on the Beverly Hillbillies. From all the pictures Google gave, she always seemed to be wearing longer pants. Not quite full length jeans, but they definitely went past the knees:
Maybe a capri or clam digger type length with a length of rope as a belt.