Duct. Duck is a brand name

Yes. But also mostly no.

Wikipedia:

"Duck tape" is recorded in the Oxford English Dictionary as having been in use since 1899 and "duct tape" (described as "perhaps an alteration of earlier duck tape") since 1965

and:

In 1971, Jack Kahl bought the Anderson firm and renamed it Manco. In 1975, Kahl rebranded the duct tape made by his company. Because the previously used generic term "duck tape" had fallen out of use, he was able to trademark the brand "Duck Tape" and market his product complete with a yellow cartoon duck logo. Manco chose the term "Duck", the tape's original name, as "a play on the fact that people often refer to duct tape as 'duck tape'", and as a marketing differentiation to stand out against other sellers of duct tape.

People should really do the bare minimum double-check before showing their whole ass.