Just to muddy the waters, this tape was developed during WW2 by Johnson & Johnson for the American military, who needed a strong waterproof tape to seal ammunition cases with. The backing cloth they used was cotton duck, a very strong cotton canvas much loved by we older members when used for saddlebags & panniers.
So thus it should be called 'duck' tape, as it was referred to by G.I.s. Why 'duct' tape - ? mishearing, mispronunciation, who knows - ?
Then there's gaffer tape; similar thing used in the entertainment industry for holding down lengths of lighting etc. cables on stages. But, gaffer tape is designed not to leave any sticky residue behind, so the difference is subtle but it's there. Depends how pedantic you want to be.