Clarification of the terms "brute force" and "guess" In the answer to the question “What exactly is a negligible (and non-negligible) function?”

There is a part in the explanation that – as far as my knowledge goes – is conflicting:


  But instead of brute force, the adversary can guess (a polynomial number of) random values and hope to chance upon the right one.


From what I understand, a “brute force attack” attempts to guess (to exhaustion)… or am I missing something here? Can someone please explain the distinction in this context?
The difference in that answer is that brute force refers to an exhaustive guessing attack (having guaranteed success but requiring exponential time) whereas guessing (a polynomial number of) random values refers to exactly what it says (requiring polynomial time but having only a certain chance of success).