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am wondering, that each char in unicode has a code point; what's the analogous term for a character in a font?

i never understood the part of the process when a decoded file needs to be mapped to font (or fonts, by some modern font substitution techonolgy)

for example, when a text editor has decoded a file from it's character encoding, and suppose there's greek alpha α (U+03B1). What's the exact process this app chooses a particular glyph in a font? most app has a prefered font. Let's say it's courier. (and what happens in the case of a rare unicode char say the heart ♥ (U+2665), that's not in the default font? How does the app know the font doesn't contain that char?)

does a font contain meta info about what symbols it has?

if 2 fonts both have the symbol alpha, do they necessarily share the same “code point”? or is it dependent on the type of font such as Type1, Type3, TrueType, OpenType? ...

thanks for any pointers or references.