I'm still glowing from that little tripod/selfie stick that I scored, that has a Bluetooth remote.
The one for Canons does indeed work for what looks like every single Canon DSLR and the Nikon looks like it works for their DSLR series.
I have one similar to this that I got years ago and it works quite well, even in direct sunlight as it uses IR for control. Just set the camera up, with either the more automatic functions or manual functions set up and then just press the button.
There are some nice tethered apps for phones and tablets that let a person remotely control their DSLR and all functions - which makes it great for microphotography, astronomy, or for photographing models - human or otherwise- and doing special effects , where you don't want to change jog the camera even a mm but need full access to nearly all functions. A good one is https://dslrcontroller.com/ They also support a new method of creating a wireless connection to ANY Canon DSLR and accessing it remotely.
Hard to say... it was a two part, techie or "transistor radio" looking deal. I went by the screenshot just now on my cell phone but it got away from me. Anyway the price was something like $27.
I have never really had anything other than a cable release for my Pentax, and a wind-up self timer for the Polaroid SX-70.
On the Canon Rebel series there is a piece of open source software that can be installed on the memory card that the camera will look for and boot, supplementing stock the OS - and which has a ton of mods, one of which is a sound activated one. I use a similar option on my phone for taking photos of myself when I am with a group of people without having to have a Bluetooth remote or use a timer, you can say "cheese" etc and it will take the shot. The one for the Rebel works well but doesn't use a trigger word and instead you set the audio level and then any sound above that level takes a photo, really useful. Take a photo by snapping your finger - or use it to photograph bullets as the gun fires, etc. https://magiclantern.fm/features.html