One important thing I repeat to myself when talking about Strains (Although I tend to forget it) is first, be sure to know which measure the book or author is using.
Note the difference in the shear component letter in the formulas:
Both formulas are the same but one is using the engineering shear strain and the second is using the strains provided directly from the tensor.
The relationship between them is this.
Keeping this in mind we could reduce some of the multiple options we have now as they are equivalent.