Is there a difference between hypnotic and hypnotizing? I believe they are synonyms but I think of hypnotic as being more metaphorical, and hypnotizing as being used, at least sometimes, as a clinical (or at least factual, non-metaphorical) term.
"Hypnotic" is a standard adjective, while "hypnotizing" is an adjective that has been created out of a verb, which is called a "participle adjective".
What that means, is that something that has the potential to induce hypnosis (literal or figurative) would be considered "hypnotic", whereas something that is "hypnotizing" is currently in the process of hypnotizing (in the verb sense, figuratively or literally) something.
The above phrase indicates a quality in a person's gaze, in that it has the potential to entrance someone.
This phrase, on the other hand, indicates that the narrator (or the character in context) is actually caught in the trap, entranced by the hypnotic gaze — or rather, that the gaze is in the process of entrancing the narrator.
There is no real reason why one should be considered more metaphorical than the other, although it could be argued that "hypnotizing" is the more common term in the literal sense, simply because it is easier to factually identify an action, rather than a vague property. Whether or not that is the case, I do not know — in truth, I always thought that "hypnotic" was the more common word.