I think Huck and Huckabuck are the same thing. At different periods they were linen, linen-cotton blend, or just cotton.
I do not think it was a definite progression like I'm writing it, however. I do think there was linen around simultaneously with the cotton.
This is just from my wanderings and experience, nothing I can read and point to.
Cotton huck toweling at JoAnn's is still a great find. Fabulous for camp use. I remember when I got on a "period bath towel" kick, for those events where we get WET (swimming, sweat lodge, etc.) and I didn't want to be the farb with the modern towel. I still have a tote box full of cotton and linen towels - some modern huck that I cut and hemmed, some modern linen towels that were too cheap to pass up, and some antiques.
Drying your entirely wet body and hair with a cotton or linen towel that is not terrycloth is so unsatifsying.
No wonder girls couldn't go out because they'd just washed their hair!