News to me. I’ve never bodged a mains electrical repair with duct tape but that’s handy to know in case I’m ever tempted and have silver to hand so thanks!
It’s a blurry line, but generally “Duct” tape was designed for sealing ducts, so is horribly sticky, great on hard surfaces, and long lasting and a bit waterproof. Usually looks like plasticy ripstop.
“Gaffer” tape is a product from film and theater, gaffer is the job title for lighting technician*. So it’s heat resistant, works on carpets as well, can be written on with sharpie, but also more temporary and doesn’t leave a residue. Usually looks like cloth. I wouldn’t assume gaffer tape to be good insulation, but I’d not use duct tape anywhere where it being conductive might be an issue.
Electrical tape – shouldn’t actually be used for insulation. It’s insulating enough that a stray tail of it contacting something won’t cause a problem, but 0.1mm of PVC isn’t going to do the same job as ~2mm, Fine for color coding wires, taping them together etc, but it’s not “insulation tape”.
*Gaffer = person with a gaff, gaff = big wooden pole, big wooden pole = the thing used to open the big skylights on the rooves of studios to let light in before high powered electrical lights were more common.