"Width" is a bit of a misnomer, as most people presume the term refers to the sole measurement (left to right). It is actually the circumference of the last, measured at the ball and other points of the last. The old term "fitting" would be probably more appropriate. In the old days a slim last was fitted-up with additional leather pieces to increase volume; this would also have increased the width of the sole with each additional 'fitting' attached.
The standard rule for the widest point of the sole is the ball measurement divided by 3 plus 10%. Let's do it metric (much easier than dividing inches) a circumference of 240mm : 3 + 10% + 88mm. The increase in circumference from one width to the next is about 5mm, which means the increase (or decrease) in sole width is about 1.5mm from one fitting to the next. Here is a drawing showing a particular last in a given size and different widths. The length remains constant, but the measurement at the widest point changes.
Most shoe factories (maybe all) do not change the sole shape with every width. The soles are dye-cut (large cookie-cutters) and it is common practice to build two shoe width on the same sole shape (the wider last is higher but not wider at the base, so the wider shoe has more volume but not in every dimension.) EG builds D and E on the same sole shape (this was once confirmed to me by an EG employee.) So E is higher than D, has more volume but is, strictly speaking, not wider than D. I presume with American shoes, although I had that never confirmed, widths C and D are based on the same insole; than a wider one will cover E and EE.
Here is a drawing from a text book (Golding, 1935) comparing a typical English with a typical American last.
The American one is wider in the base and shallower, the English one narrower and higher, giving both of them (more or less) the same circumference. I believe that distinction is still the case: American shoes are shallower (some of the Alden loafers can be extremely tight across the instep). So the EG shoe in D (same sole shape, but shallower last) will be closer to the American ideal, than the English E width; the American E width will be wider in the base than the standard English E, but they are quite close to each other in circumference.
I say that with reasonable, but not absolute, certainty as I have not access to the different individual last and so cannot get confirmation by runnig a tape measure over them. But I do not think, that I'm too far off.
This makes perfect sense, which is probably why English shoes fit me better because of my higher instep. Thanks, Bengal.