While the term "duct tape" does commonly refer to both the (usually) grey fabric based tape and the aluminum foil based tape used in duct work, technically only the aluminum tape is duct tape.

The proper term for the fabric based tape is actually duck tape as it was originally made from cotton duck, which is a durable cotton weave similar to denim or canvas that can be easily made water resistant by impregnating it with wax. It was invented during WWII and was used to seal ammo cans. It's also not particularly resistant to extreme temperatures nor is it air tight, and is kind of useless when it comes to duct work.

Duck Tape is also a name brand for both duck tape and duct tape.

Duck tape is named because it was originally made using cotton duck, which is the finer grade of canvas. Today it is made using scrim and plastic backing, while gaffer tape is closer to the original duck tape.

In the mid 20th century people started referring to it as duct tape as they mistakenly believed that as it was starting to be marketed for that use (including new silver variants to blend in with aluminium fittings), it must be properly named “duct tape”.

They call it duct tape because it sounds like duck tape which is the name brand. If it's labeled duct tape then it's just the generic version. Actual duct tape is foil tape or mastic.