Dear Gaya,
Referring to your question
Aren’t those 2 things the same? (With a different formula)
it is worth to say that 5.11.2 presents formulas valid for the particular case of Wind Load Calculation.
That is why for this calculation the liquid weight (wL) is the weight of a band of liquid at the shell using a specific gravity of 0.7 and a height of one-half the design liquid height H, exactly as 5.11.2 Unanchored Tanks says.
So the numerical coefficients in 5.11.2 formulas are already amended by this assumption.
Best regards.