The disks you are talking about needs to be purchased. If you are visiting you may find it hard to find an open spot selling those off business hours. It’s less convenient then coin operated parking meter.
I think every car in Europe has this parking clock/disk.
If you do not have the clock, then piece of paper and written time is also OK.
I definitely rented a car in Switzerland before pandemic that did not have the disk and I had to buy it at some tourist info center.