In the CTR mode, a nonce, a counter value and the key are needed to form the input of the PRF. However, the Deterministic counter mentioned in Dan Boneh's slides (https://crypto.stanford.edu/~dabo/courses/OnlineCrypto/slides/04-using-block-v2-annotated.pdf, pp. 20), does not have the nonce. It only uses the key and the counter value as the input of the PRF. If I'm not mistaken, we can say that given a PRF $F$ and a key $k$, a pseudo-random number is generated by $F(k, g(nonce, counter\_value))$ in CTR mode, while deterministic counter mode uses simply $F(k, counter\_value)$, without the presence of nonce.
According to the slides pp. 21, Deterministic counter mode is already semantically secure. So why do we need a nonce in the standardized CTR mode?