I think the description of each in the documentation makes this very clear:
$ cookie just gives you access to cookies, as if you were doing some other method.
$ cookieStore uses cookies to create a key / value storage solution for you.
So, if you are starting something new and want to save key / value pairs, use $ cookieStore
If you want to use the existing solution for cookies - download files for reading / writing from the existing system of server sessions, use $ cookies.
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