Curious in the Strict example, what happens if you arrive from another Site (so no cookie is readable) and you do something that sets a cookie? Have you split

Curious in the Strict example, what happens if you arrive from another Site (so no cookie is readable) and you do something that sets a cookie? Have you split the universes? Is there now an alternate reality of some kind? To read that second cookie, do you always have to arrive from the first site?