A difficulty in understanding the operation of a Turing machine on a certain language.

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The implementation-level description of Turing machines that decides the following language over the alphabet {a,b,c} is given below.

enter image description here enter image description here But I feel that the state diagram and the set of configurations will give me more subtlety in understanding, could anyone suggest a book for me that contains this? or could anyone explain it thoroughly for me?

Also, I could not see the difference between the above The implementation-level description of Turing machines and the one given below:

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Why both implementations are right?

Thanks!