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Both methods are possible. You can copy an existing disk to another disk and then install that disk into the host machine so long as the original disk is operating or by using a complete image that was made prior to failure. This takes special software to complete. It is also possible to restore a backup to a new machine. This is called a bare metal restore and also requires specific software and knowledge so that you can inject the required hardware drivers of the new system into the old image. Both are dependent on what was used to create the backup.
When moving from one machine to another newer machine it is often best practice to backup the original and only to restore the user data from the user's profile folder to the new machine. At which time you reinstall the user apps and reset your preferences on the new pc. you can locate your user folder by opening the windows file explorer and typing the following: %userprofile%
Enable hidden files and folders and copy everything you see to an external disk. I would also back up any installed programs home folder located on the disk.
Disk2VHD is a nice Microsoft utility that can backup an online disk and push it to a file on an external disk that can later be mounted or used to restore to another disk.

https://docs.microsoft.com/en-us/sysint ... s/disk2vhd