The A and the M refer to how the stopping down of the diaphragm is controlled, not to exposure.
Long, long ago, in the dark ages, automatic aperture, which is the norm today, did not exist. This means that the aperture was directly controlled by the f stop collar on the lens, completely independently of the camera body/shutter. If you set it to wide open, the aperture was wide open. If you set it to f/8, the aperture was at f/8. This means that on an SLR camera, if one wanted to compose and focus wide open, but shoot at another aperture, one had to open up the diaphragm to focus, and close it back down by hand before shooting, and open up again to compose and focus the next shot. This is manual aperture, and the Mamiya allows you to set the diaphragm to work in this way.
Automatic aperture means that the setting on the f stop collar is not a direct control of the aperture, but is a pre setting. It does not actually affect the size of the aperture until right before the shutter opens. The aperture remains wide open until you fire the shot off. Then, after the shot is taken, the aperture opens back up. A mechanical or electronic linkage between the camera body and the lens tells the aperture when to stop down and reopen. This is the standard way most SLRs have operated since the SLR in general came into prominence, though there are exceptions.
Pentax cameras have the switches as well.
So, when you see a manual focus lens that has the word "auto" as part of its name, it is in reference to the way the diaphragm is controlled, not to focus or exposure.