There is a lot of misunderstanding out in the world of photography about focal length, aperture, field-of-view (FOV), and depth of field (DOF). If there's one thing I hate arguing about, writing about, and educating people about, it's these topics—especially DOF. Misunderstanding of DOF is ineradicable. Arguments always follow assertions about it. It was that way in 1910, and 1940, and 1980, and it's that way now, and it will be that way in 2030 and 2050—regardless of what I or anybody else might say about it, now or ever. I edited a technical magazine about photography for six years; take my word for this.
When "translating" a focal length, all we're doing is bringing back a FOV crop to a context that is more or less readily understandable to people because it's familiar and/or standardized. With digital's multiplicty of format sizes, it's become conventional to "translate" FOV crops into 35mm equivalents—and it amazes me that anyone still questions this, since it's a widespread practice with digicams, many of which use the 35mm equivalent focal lengths in their menu systems or even engraved on their lens barrels.
When I write that a 150mm ƒ/2 lens on 4/3rds format is "equivalent" to a 300mm ƒ/2 lens in 35mm, no, the actual focal length of the lens hasn't changed—it's still 150mm. And no, the aperture doesn't change either. You don't have to "translate" that ƒ/2 to ƒ/4 or ƒ/5.6 to "be consistent." There's one thing that does change, and that's DOF, and yes, you would have to stop down the lens on the larger format to get the same DOF for identical scene FOVs—but aperture is not primarily a control of, or a measure of, DOF; it's primarily a measure of exposure. It's highly misleading to say that a 150mm ƒ/2 lens in 4/3rds should be "translated" to a 300mm ƒ/5.6 in 35mm just because the DOF of those two apertures might match more closely. DOF is a "side effect," one might say. As an exposure control, ƒ/2 is ƒ/2 is ƒ/2. For a given exposure, aperture is independent of format.
When "translating" focal lengths, all we're talking about is FOV. It's true that it's not rigorous. We do it that way because we don't have a better way to do it. We don't all have any other concept in common. And it's not even possible to come up with a completely rigorous scientific nomenclature, because aspect ratio matters as well. If you want to "translate" lens focal lengths as a means of understanding FOV between, say, 8x10 film and 35mm film, you have to choose whether you're going to compare the long dimensions, or the short dimensions, or the diagonal measures—and none of the three results in an exactly accurate equivalence.
For myself, for instance, I always compare the longer dimensions of different formats to each other, but that's because that's how I see. How "wide" a lens is to me depends on how much it takes in from side to side, not on its height when held horizontally.
So let's say I want to know what a 110mm lens on 2 1/4 square format would be in 35mm terms. A square MF neg has an image area of 56 x 56mm, so I'd compare the long dimension of the 35mm film to the square and I'd "translate" the focal length/FOV to about 70mm in 35mm terms. There would be some height "added" to the square, is all. (When Lee Friedlander was asked how the Hasselblad he switched to was different than the Leica he previously used, he said something like there's more sky.) But someone else might be more sensitive to image height. That person might compare the short dimension of the 35mm frame to the square, and might be more comfortable thinking of that 110mm lens as being "equivalent" to about a 50mm lens on the 35mm, but with the ends cropped off!
Who's right? Neither, obviously. (Well, actually, both, but neither more than the other.) And to compare the film diagonals is not completely rigorous either, since that's just a rather crude means of splitting the difference.
The point is that it's just best not to get too bent out of shape with FOV "equivalents" and focal length "translations" and all the attendant issues that come up in their wake. It's just a rough, seat-of-the-pants means of giving you a general idea of the angle of view the lens is going to take in. It's no more important than that. And that really isn't worth arguing about.