So the Pixii II framelines marked 28mm, 35mm, 40mm and 50mm are just approximations for when using 18mm, 24mm, 28mm and 35mm M-mount lenses?
Godfrey already has ably covered the basic answer (i.e. "no") but I'm going to deliver myself of a more detailed explanation because I've been trying to straighten this out for people ever since I got my Epson R-D1 in 2004!
Concept 1: The focal length of a lens is a simple physical property that can be measured exactly on an optical bench (or approximately with a ruler): It's the distance from the optical center of the lens to the focal plan when the lens is focused on an object at a distance of "infinity" (the sun works well as long as you're careful to avoid burning anything important!)
Concept 2: You can see from this that focal length alone doesn't tell you anything about the lens' angle of view or area of coverage; that depends on both the image size (the specific lens needs to be designed to cover that image size, of course) and also on the focal length itself.
Back before photography was ruined by the Internet, everybody understood that, for example, a lens with a focal length of 50mm was a telephoto on your Bolex, a "normal" on your Contax, a wide angle on your Hasselblad, and an ultra-wide-angle on your Linhof (no, there wasn't a 50mm lens that covered 4x5-inch film, but there WAS a 47mm Schneider Super-Angulon that did.) Nobody confused themselves with irrelevant notions of "equivalents" or "crop factors."
What really counted was how wide a subject area you wanted to cover in your photo. Mostly for reasons having to do with geometric perspective, the convention was to say that a "normal" lens is one that covers an angle of about 40 degrees along the long side of the picture. (Spread out your index, bird, and ring fingers as wide as you can, and the angle they cover is about 40 degrees; use this trick to amaze your friends on photo walks.)
Since what's in front of the lens and what's behind the lens always form similar triangles (everything in the same proportion) you can do simple trig to find out what focal length you need to achieve this "normal" coverage angle on any image size you like. Got your spreadsheet handy? Then type in this:
([long side of frame]÷2)÷TAN(RADIANS([angle of view]÷2)) gives you the focal length of lens you need.
For example, on the Pixii the long side of the imager measures 25mm, more or less, and the formula tells you that a lens with a measured focal length of 34mm will give you a 40-degree angle of view. For a Moses-format camera with an imager that measures 36mm along the long side, you'll need a lens with a focal length of 49mm. If you have one of those Fujifilm or Hasselblad cameras with an imager that's 44mm along the long side, you'll need a 60mm focal length to cover 40 degrees, and at the other end of the scale a Micro Four Thirds camera with a 17.3mm image width will need a 24mm focal length to cover 40 degrees. (And yes, let's round up 24 to 25, 34 to 35, and 49 to 50 for the sake of neatness.)
The same simple calculation works with any other angle of view you might want to cover, so you can easily work out for yourself that if you want to cover a 75-degree angle (for example) you'll need a focal length of 12mm on your Micro Four Thirds camera, 16mm on your Pixii or R-D1, 24mm on your Moses-format camera, and 30mm on your 44x33mm camera (all rounded for neatness.)
Yes, you can look at those numbers and say "this is equivalent to two times that" and "this is equivalent to one-and-a-half times that", but that makes just as much sense as telling people your new Tesla's range in terms of horse-equivalent furlongs per peck of feed. (In the days of horse-drawn streetcars, the streetcar companies worked this out in fine detail so they'd know what to budget for feed, so if you want to web-search old documents you can work out "horse-equivalent range" fairly easily... it's just kind of a loopy exercise because no one will know what you're talking about.)
To recap: If you've got an M-mount lens with a marked focal length of, say, 28mm and you put it on your Pixii, you set the Pixii's finder to its 28mm setting, and the viewfinder frames will show you the approximate area that will be in your picture -- in this particular case, an angle of 48 degrees along the long side of the frame. Same for a lens with a marked focal length of 35mm, 40mm, or 50mm -- set your Pixii's finder to the marked focal length and it will show you the framelines that indicate the correct area of view.
