If you're on Mac or Windows, there's no difference. On Linux they are different.
If you only work in Vim, you really don't need either of them (I mean that you can live without them), as they are best used to interact with the outside world.
Indeed, if you select something with your mouse (everywhere, not necessarily in the terminal; try by selecting some text in, say, Firefox), and then you go back to Vim, the *
register will contain that thing you selected.
If instead you copy some text with Ctrl+C or equivalent (again from anywhere), and then you go back to Vim, you will find that stuff in the +
register.
Clearly, if you select some text with your mouse and then you hit Ctrl+C to copy it, and then you go back to Vim, you will find the same content in both registers. There are ways, however, to copy something to the clipboard without selecting it first (think about the "copy to clipboard" buttons that you sometimes find on a website), and in those cases you can preserve the primary selection while writing to the clipboard.
BTW, in case you don't know, :reg
shows the commentcontent of the registers.