I grew up using SAE wrenches, and always grab my 7/16" wrench when working on a 1/4" nut or bolt, 1/2" for a 5/16" and so on.
On my introduction to Whitworth/BS wrenches, things just made more sense. If you have a 1/4" bolt, grab your 1/4 BS wrench.
Back when Mr. Whitworth developed a standard bolt system, he experimented with different thread pitches and angles, finding which worked best for the materials on hand. He then determined the optimum head size - that bolt head which provided the most holding power for a given bolt diameter. The result was the Whitworth system. Decades later, when materials improved, British engineers re-examined these parameters, and found that the new materials didn't need such large heads, and a head one size down on the Whitworth scale was nearly ideal. This is why a 3/16BS wrench is a 1/8W. This allowed all those Whitworth tools out in circulation to continue to work.
A/F was developed for the export market, and A/F nuts and bolts will work with SAE, except the thread angle is not identical. A/F simply means 'across flats', which is how SAE wrenches are sized - measuring across the head of the bolt from flat to flat.
