Here is an article that detail the difference.
One of the interesting part is the following
The biggest single difference between the systems is where they store
the information. For Shadow Copies, the old snapshot blocks are almost
always stored on the same volume as the current, up-to-date file.
Technically, it is possible to store them on different volumes, but in
practice, this is rarely done (and, in any case, was only ever
possible on server versions of Windows).
This has two important repercussions, one very good, one very bad. The
good repercussion is that the system is self-contained. The only thing
you need is a hard disk; it can contain its own historic versions. The
bad repercussion is that it's self-contained: if that hard disk should
stop working, you lose both the current files and all the previous
File History, on the other hand, never uses the same disk to store
historic versions—it requires the use of either a network share or a
separate physical disk. (Again, technically that's not quite true, as
you can use a file share hosted on the same physical disk as the one
being backed up, but this defeats the purpose). This means that if the
disk should fail, the backups should all be safe. You can recover the
backups simply by installing the operating system to a new hard disk,
giving the system the same name as the broken one, and using the same
location for File History; the history will pick up exactly where it
One consequence of this is that the File History storage location
might not be available—if you use network storage on a laptop
computer, for example. To cope with that, the system can additionally
use a portion of the local disk as a cache into which it will make
replicas whenever the history location is unavailable. As soon as the
history becomes available (so as soon as you return to your home
network or plug in your history USB disk) the cache will be copied to
the history location.
File History only tracks files in certain locations; Libraries, the
Desktop, and a couple of other places. Shadow Copies, in contrast,
track almost the entire disk. This means that if you keep your files
in an unusual location, File History won't protect them. While files
in the protected locations can be excluded (to, for example, avoid
burning lots of space on podcasts or other readily re-downloaded
data), there's no provision to include extra locations.