Normally umount is for fixed drives. ( Hard drives )
eject is for "removable" devices. DVD's, CD-ROMs, USB sticks, etc...
But another big difference is that often Linux (most Os's in fact)
lie to you. For example if you are using Nautilus or some GUI file manager,
it shows a blue line when you copy the file over. When the blue line
(or whatever color it may be) reaches 100%, you assume the file is copied.
But it isn't always. It's just copied to to a memory cache.
When the OS has more free time, it will "really" copy the file over to the
USB drive, (or whatever you are copying the file to). You can force the
disk to umount or eject before the file is actually fully copied over.
There are some tricks to make this not happen (turn off disk caching)
But if you've ever pulled the USB stick out after the blue line was finished,
but before "eject" gives you the "safe to remove", your file is likely corrupt
or missing.