Is it Duct Tape or Duck Tape?

One of the most useful inventions ever is called Duck Tape or Duct Tape.  The earliest version appears to have been made from cotton duck cloth sealed with linseed oil and used to water proof things, and first appeared in the 1890s.  Later versions used rubber or various other flexible, water resistant coatings, mostly over cotton duck.  The Revolite division of Johnson and Johnson made a version that was easy to tear, so you didn't need to use scissors or a knife, and was used to waterproof ammunition cases during World War II, and became widespread among the troops for this and many other uses.  This stuff was found to be so useful that other manufacturers started making copies.

The fiber reinforcement makes the tape very strong, and the plastic or rubber makes it relatively water resistant, depending upon the adhesive used.  It's traditionally shiny grey although it can be obtained in just about every color imaginable, including transparent, and printed patterns, and it's usually 2 inches (50 mm) wide, although other widths are available.   Some time around 1960, the name somehow became conflated with the tape used for sealing furnace ducts.  This is one of the very few things it's not particularly good at: the heat tends to make it dry out and become brittle over time.   There is heat resistant foil tape which is actually the right thing for this.  Nevertheless the name change stuck, and a company was able to copyright the name "Duck Tape".

Present versions are usually based on a thin "scrim" which is a loose weave of some sort of fabric--all sorts, cotton, rayon, nylon, even fiberglass, depending upon the strength needed, and the grey part is usually Low Density Polyethylene (LDPE--type 3 plastic) colored with aluminum powder.  The adhesive is generally relatively strong, but relatively cheap, and tends to leave a sticky residue behind when it's removed.  Gaffer Tape is a variety that doesn't leave a sticky residue and is reinforced by stronger fabric, so it needs a knife or scissors to cut.   Preservation Tape is a variety that doesn't leave the sticky residue and doesn't have much or any reinforcement, so it's easy to tear.  Speed Tape, sometimes called Racer Tape,  is a variety that has a smooth surface and strong enough adhesive to tolerate the high wind of a racing car or airplane.  There are 100mph, 200mph, etc., versions.   It's sometimes used to make temporary repairs to airliners before a more permanent repair can be made.

There has been at least one roll of Duct tape on every US manned space mission since Gemini, and it played a major role in the rescue of Apollo 13.  It was also used to extend the fenders on the moon rover on Apollo 17 when they sprayed too much moon dust around.   It works, at least for a little while, in the vacuum of space.

It is most correctly called "Duck tape", although because of the copyright, it might have to be called "Duct tape" sometimes.

It is, as Red Green says, the Handyman's secret weapon.