3.323 In colloquial language it is common for the same word to signify in different ways – and thus belong to different symbols --, or for two words, that signify in different ways, to be applied in a proposition in ways that are the same externally.

Thus the word “is” appears as the copula, as the sign of equality, and as the expression for existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak about something [an object], but also about something happening [an event].

(In the proposition “Green is green” – where the first word is a person’s name and the last is an adjective – these words do not simply have different meanings but they are different symbols.)

Russell in Logical Atomism: “The is of “Socrates is human” expresses the relation of subject and predicate; the is of “Socrates is a man” expresses identity. It is a disgrace to the human race that it has chosen to employ the same word “is” for these two entirely different ideas—a disgrace which a symbolic logical language of course remedies.” (p. 172)

Some clue here about Wittgenstein’s use of “external.” It refers to the extra-logical, the merely physical, the superficial. Why not say simply that “Green” and “green” have different meanings? See PI §558 and §561.