Some use classic Bluetooth, some use Bluetooth low-energy. Some require their specific dongle for pairing, others will pair with the Bluetooth already built into a PC.

Lots don't use bluetooth at all!

That all sounds rather hit-and-miss 

How is it hit and miss? If its a bluetooth mouse then you use a PC with bluetooth, usually used on tablets and phones that have bluetooth in them already since you have another input method for when bluetooth doesnt work.

Propriatary ones present as a standard USB device, so use a port, but have no need for any pairing etc beyond what they do at the factory between the USB reciever and the mouse/keyboard. Some like the logitechs let you repair them yourself to other dongles since running multiple on a PC seem to cause RF interference issues.

OK, so leaving aside infra-red devices, all cordless mice and keyboards can be called "wireless"?

Additionally, some require their own proprietary accompanying dongle, and those marked as Bluetooth can be both workable with the computer/tablet built-in receiver, whilst others may need their own (albeit still Bluetooth) dongle?

ive used both the wifi dongle ones and the bluetooth ones, both have pros and cons.

Bluetooth pros: no doongle

cons: then device is in airplan mode you can use it
saps the batteries pretty quick
more expensive

dongle pros: cheaper
longer battery life
not affected by airplane mode and can wake device (laptop) from sleep

cons: can wake device from sleep
little dongle can get in the way/damaged

Im running bluetooth at the moment as the dongle annoys me as i tend to put my laptop into a bag a bit and it just gets in the way

to answer your question yes, but i havent seen one with a bluetooth dongle, they assume you already have bluetooth

there are very few bluetooth devices from logitech and microsoft (the main brands at the appliance store)

Some are dual mode, the idea being that bluetooth is used with your tablet and the dongle with a PC.

Bluetooth ones seem to have greater latency than the logitech dongle ones, but neither is as good as a wire. Ive not tried any of the logitech gaming wireless mice because ive already got a nice razer one, but if its gaming it should be better. They usually recharge off micro USB since they have much higher power use than a laggy desktop use one.

Thanks people, comments appreciated.

as an aside, my daughter has a newish laptop with Bluetooth built-in, and then acquired a cheapy Bluetooth mouse.  We can get the computer to recognise that a Bluetooth device wants to connect, and even says it is 'installing' device, but it don't work thereafter.

I tried the mouse on a desktop using a Bluetooth dongle that I know works (connects to phone and transfers images etc), and the same thing happens.

Dud mouse, or something else?

Check device manager for a ! on anything. It may have not actually installed the mouse part of it properly.

If its a genius bluetooth mouse, check the way the batteries are put in the mouse.

     >Check device manager for a ! on anything.<

Did all that, no Bluetooth or extra device shows up on either the laptop (Win 10) or desktop (Win 7).

Extra bonus point question:   Some computer manufacturers (e.g. Dell) advertise systems that include wireless keyboard and mouse.

Would that be proprietary wireless, or Bluetooth?

Rickles:

 

Extra bonus point question:   Some computer manufacturers (e.g. Dell) advertise systems that include wireless keyboard and mouse.

 

Would that be proprietary wireless, or Bluetooth?

 

Could be either. Those ones will often have bluetooth but a special bluetooth reciever that can present as a keyboard and mouse to operating system installers and similar without their own bluetooth stack.

I bought a MS Designer bluetooth mouse over Christmas, seems to work fine for general computing, paired up with laptop, tablet, phones etc, picked it up on special for 30% off so was only something like $32 or so ($45rrp). It is also quite a low profile design so comfortably fits in small laptop bags