However, my understanding that the original term was “duck tape” which latter shifted to duct.

Duct Tape vs. Duck Tape – an explanation

Is it Duct or Duck? We don’t want you to be confused, so we will explain. The first name for Duct Tape was DUCK. During World War II the U.S. Military needed a waterproof tape to keep the moisture out of ammunition cases. So, they enlisted the Johnson and Johnson Permacel Division to manufacture the tape. Because it was waterproof, everyone referred to it as “duck” tape (like water off a duck’s back). Military personnel discovered that the tape was good for lots more than keeping out water. They used it for Jeep repair, fixing stuff on their guns, strapping equipment to their clothing… the list is endless.

After the War, the housing industry was booming and someone discovered that the tape was great for joining the heating and air conditioning duct work. So, the color was changed from army green to the silvery color we are familiar with today and people started to refer to it as “duct tape*.” Therefore, either name is appropriate.