This question might be on the edge of what is allowed, since it might be quite difficult to answer this with facts and reason. If this crosses the boundaries please let me know. The reason I decided to ask this question anyway, is because I feel that we could have a discussion that is based around clarifying the boundaries of each definition. I think this is a topic that most of us understand intuitively, but I struggled when I tried to put it into words.
What I am trying to understand is where the boundaries lie between what is considered an alphabetic character (or any other (phonetic) character for that matter) and its typeface. I find each of these individually already hard to define, but will give it a go regardless. I think a typeface is the shared design between a set of characters. The alphabet is a standardised set of symbols to express a certain sound. Where I think things cause friction is in how standardised these symbols are. For instance if you look at writing cursive, the way the letter 'f', 'r' or 'a' is written is quite different than in the font of this website.
The obvious thing to say would be that everything that is shared between the fonts is what would be considered part of the alphabet, and the rest part of the typeface. But I feel that this is more like a rule of thumb that works in most cases, but not all. As I am not a graphic designer I feel that there is surely a better explanation out there. So that is why I am reaching out to you.