Since you are recovering pictures, means there is an issue with the drive, otherwise what's the recovery for?
If there is an issue with the drive, it can very well not be readable by the second system.
Or the USB enclosure you got is not working properly.
You can try to use a program called testdisk to get the partition back on the drive if there is an issue with that. http://www.cgsecurity.org/wiki/TestDisk
Does not sound like the ownership issue Area51 linked, that would not give you a "not formatted" message, you'd be able to see the files, but can't get to them.