The OS on Big Sur is read-only and cryptographically signed. When you do an update it has to download and replace the whole thing. There are no “updates”.
However due to the magic of snapshots on APFS, it can do this on a separate copy and do an instant switcheroo when it’s finished.
So your first computer had to do the work while you waited. Your second computer had already done all the work and just needed to switch the OS volume for the new one.