A lot of these terms get used interchangeably, or have variations on how they're used in different communities. For example, once you start talking about "building a history", a lot of people I know will start to label that as a version control system ([VCS](https://en.wikipedia.org/wiki/Version_control)), which they'd consider a type of archive. That kind of overlap is always going to exist when it comes to file management tools.
In my experience, "file of record" is what separates an archive from a backup. For a backup, the local copy is the best file to have, and any additional backup copies (whether identical or older versions) are lesser. For an archive, the local copy is the lesser version, and it can/should be replaced as needed with the item in the archive. So, in some ways, if you get a file from an archive, you've created a backup of it.
So it sounds to me like you've got a 1TB archive that gets updated by your laptop and backed up to your 2TB drive. If you add cloud storage into the mix, you have to decide what role it plays. For me, the cloud is a (partial) backup of my archives.
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