I don't think the calculations use the same equation.... Looks like the difference between the classic ABV formula and the more precise alternate equation to me. The first calculation you mention assumes a FG of 0° Brix (Plato, but the two measurements are essentially equivalent) using the alternate equation and I get 11.49%. Using the SG figures you mention in the second scenario, I get 8.4% using the standard equation. So no, for the scenarios you outline, the results should not match. Here's my recommendation:
- Use the Alternate Equation for higher gravity brews (like yours). It's more accurate.
- Whether you use Brix/Plato or SG, always enter both values (OG and FG)