Is there a single valid definition for a Turing Machine, or is it mutable?
The ordering of the items in the 7-tuple M is completely immaterial to the behavior of the Turing machine. There is no "correct" or "incorrect" ordering; but I would say that both orderings are essentially the same definition. And I don't see that the blank character is treated any differently in the two definitions. In both, it's part of the tape alphabet but not the input alphabet.

For the two definitions to be effectively different, you would need to find a difference that does not correspond to a re-ordering of the 7-tuple, or is just in the wording of how the blank symbol is treated. 

The only actual difference between the two definitions seems to be that your book has $q_{\mathrm{accept}}$ and $q_{\mathrm{reject}}$ as the halting states, while Wikipedia permits a general set $F$ of halting states. This is because your book only deals with Turing machines that compute languages (so for every string $x$, either $x \in L$ or $x \not\in L$) while Wikipedia also wants to handle Turing machines that compute functions. For a Turing machine that computes a function, you can assume that there is only one final state, $q_{\mathrm{halt}}$; the value of the function will be written on the tape when the Turing machine halts.