Your cp destroyed whatever filesystem there was on the external disk because you copied to the device itself without mounting it first. To fix:
format the external disk on the other Mac (HFS+ should be fine)
boot old Mac into single user
mount the external disk (mkdir /Volumes/mydisk; mount /dev/disk1s2 /Volumes/mydisk)
copy the files to the mounted disk (...
I had the same problem. I tried this: I tried to reformat the USB drive on the Windows 10, but this time I hit the button 'Restore device defaults' and selected 'Default allocation size', and it worked. I was then able to access the drive on the Macbook.
For this specific error, do the following-
run Disk Utility/ First Aid a few times. There are cases where it may fix a bit of your partition map but still be unable to mount the partition containing your data, until run a few more times, this does look like a software rather than hardware issue
If you're running a very new Operating System and the drive was ...
The obvious cause is the filesystem or physical media can not make changes so make it reliable. Also, there are many different filesystem types and drives, so be sure your tool supports your OS and Hardware if you don’t try them for free first.
Do you have a backup? If not, do that immediately. You may need recovery software for this if the mechanism is ...