The terms relaxed, acquire, and release refer to how an atomic operation is ordered against other accesses to memory.
Counter to what the article states, a relaxed atomic is still atomic, meaning that it cannot tear and, for RMW atomic, no other access can go between the read and the write. But a relaxed atomic does not order other accesses, which can lead to unintuitive outcomes.
By contrast, once you've observed another thread's release store with an acquire load, you're guaranteed that your subsequent memory accesses "happen after" all of the other thread's accesses from before that release store -- which is what you'd intuitively expect, it's just that in modern systems (which are really highly distributed systems even on a single chip) there's a cost to establishing this kind of guarantee, which is why you can opt out of it with relaxed atomics if you know what you're doing.