Ordinarily in English, adjectives directly describe the noun being modified; thus an adjective indicating an emotion attributes that emotion to the noun - "I am happy" means that I am the one experiencing happiness. But if I say "it was a happy day", I am not claiming that the day experienced happiness - it is not a conscious entity. To my mind, these are two entirely separate functions performed by the same word "happy".
In other languages, adjectives (or what might reasonably be labelled as such) commonly work this way - I have often seen native speakers of Chinese or Japanese confuse the English "scared / be afraid" with "scary / be frightening" because (as I understand it) in those languages, both concepts would ordinarily be expressed with the same word, inflected the same way.
Yet as far as I can imagine at the moment, English does this only in very limited cases. I may be scared, but the cause was scary. I may be hungry, but my food is not - and neither is my mealtime, nor anything else related to my proposed solution to hunger.
Am I overlooking something? Is there a term for this way of using adjectives in English, and are there a bunch more examples that aren't coming to mind at the moment? Or is "happy day" just a magical set phrase that I've been using unquestioningly all these years?