I really need to retrieve data of my other laptop and can wait no longer for my friend to come help. Reading up on the process (I'm stuck in emergency mode) I am slightly confused if I need to use Rufus instead of UNetbootin when reinstalling from USB.
There are basically two alternatives to retrieve the data of your other laptop using a USB boot drive.
Live-only USB boot drive
Run the USB boot drive live (live-only) and retrieve the data of your other laptop into an third drive, for example a USB hard disk drive or SSD.
In this case you can use 'any' tool to create the USB boot drive.
In Ubuntu it is easiest to use the Startup Disk Creator.
In Windows you can use both tools that you suggest in the question, Rufus and Unetbootin. Both are good tools.
In MacOS Unetbootin is a good alternative.
Persistent live USB boot drive
Run the USB boot drive persistent live and retrieve the data of your other laptop into the USB boot drive itself.
In this case I would recommend the methods described at this link, particularly the methods to get a
casper-rwpartition (and use the whole drive space),
If you use a method that creates a
casper-rw file, it will be limited to 4 GiB which is the maximum file size in a FAT32 file system.