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The morning star and the evening star (Frege's senses) are Venus (Frege's reference), as simply as the rising sun and the setting sun are the sun. All these are natural ideas of intersection and analogy regardless of cultural words.
That is to say, Frege's divide of sense and reference is as needless to say as that the sun rises east and sets west, or that it is bright and warm.
He does note (morning star) = (evening star), but does not note (morning star) ≠ (evening star).
The morning star is one thing (or referent if you like) and the evening star is another, however analogous both may be. "Everything is an analogy," as per 1974/Pirsig. That is, it is different from, and similar to, everything else. It may be marked by an identity in isolation but by too variant relations in context for a symbol to symbolize magically consistently or objectively. So the pure symbol-referent match without the mediating mind is a myth rather than a must, as illustrated by the triangle of reference on the right.
Both Mill and Frege were perhaps misguided by the "word magic" refuted by 1923/Ogden. It works no magic to refer direct but refer the mind to a thing, to be precise. Cognitivism should overcome this verbally trivial gap.
As a logician like J. S. Mill, he also looks like a word magician, textualist and externalist. Whatever is external, whether sign or design, however, is to be interpreted, whether common or uncommon. We intercept and then interpret signs and designs rather at will, whether common or uncommon.