A turing machine is defined as a set of symbols which it can read/write to the tape, and a state machine which maps the current symbol read to the next state and some actions.

The symbols of the Turing machine are atomic. They are not composed of any simpler parts. If one of the Turing machine's symbol is the letter "A", it's the letter "A". It is not, say, the ascii code (1000001)

1000001 could be the Goedel number for "A", but its not the symbol "A". The two strings "A" and "1000001" are two different strings.

Its a map-vs-territory kind of thing. If you are really good at programming--which is to say, you are really good at Goedel mapping your problem to integers--you might, by years of long familiarity, just start thinking of them as one and the same, but they are not.

It might make it vivid to consider a turing machine whose symbols were {1, 0, A}. Clearly, the string "1000001" and the string "A" are two different outputs for this turing machine. The lengths of the strings "1000001" and "A" are different. They are composed of different symbols. They are absolutely, positively, not the same string, so they are not the same thing.