Both the versions of the formulae mean the same thing. They are just using different notations.
For example:
In this, x describes the elongation of the spring and is measured as the increase in the length of the spring.
In this, delta x is the change in length of the spring. Elongation in the spring and the change in length of the spring are the same thing but denoted using different notations. The numerical value of both is the same.
The reason for the next formula is the same.
It all depends on how the notation has been defined.
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