By definition, 1 kilobyte (kB) is 1000 bytes, while 1 kibibyte (kiB) is 1024 bytes. If you see kiB marked as kB then file a bug report, kiB and kB notations are not interchangeable.
My Dolphin file browser (Kubuntu) uses kiB, MiB, GiB by default.
On the same PC, Nautilus (now called "Files") uses kB, MB, GB by default.
In regards to file size, there is yet another difference: between size of file, and size on disk. Then, there are hidden and system files, which might be copied or not, depending on what tool is used to make the copies.
Size is a good indicator to check if a copy has ended, but not very good for errors. A checksum like 'md5' or 'sha', or maybe something else, could detect errors better. Checksums can be run to check a whole tree of files at once.
If you want to be sure about the content, then don't bother checking the size, use a checksum instead.
Some CD/DVD copy protections may include intentional burnt errors, those can not be ripped by direct sector readings or by disk rescue tools.