The "English" terms?
Can you please specify the dialect of English you're referring to, instead of falling for the obviously ridiculous notion that there's one English.
I have never heard "quarter of 12", and wasn't aware it was a thing. In Ireland - Hiberno-English, Irish-English, whatever you like - I've only ever said and heard "quarter to 12" for 11.45.
So, serious question: who says "quarter of 12"? It sounds makey-uppy and illogical, so I'm supposing it might be a linguistic development in the old U.S. of A. I don't feel like I've ever heard it in movies or shows though, in spite of having been subjected to a certain amount of U.S. cultural produce, so this is somewhat mysterious to me.
Please, someone englighten me!