Duck Tape is the brand name of the original product. "Duct tape" is the generic name that the industry settled on.
("Duck" refers to the water-resistant nature of the tape. Duct doesn't actually mean anything other than sounding like "duck". Ironically, duct tape is the wrong type of tape to use on heating ducts.)
If you're going to be pedantic, then get it right. ;-)
Reading Wikipedia's article has me questioning the information in my above post.
According to Wikipedia, the name comes from it being manufactured from "cotton duck" (not because water rolls off it like a duck). Then a derived product became popular for wrapping air ducts, and the name evolved to duct tape. Then someone trademarked "Duck Tape" and revived the old name.
I'm not sure anymore about the true origins of the terms, but I still maintain that "duck tape" and "duct tape" are both acceptable names (trademark issues aside).
Wow, I always thought it was duct tape because it was originally made for taping ducts. And that duck tape was just a brand name like gorilla glue. Thanks for that.