why the heck should shooting in manual mode be different from A or S mode?
in A mode you choose aperture and the camera chooses the shutter speed based on ISO settings, exposure compensation settings and the reading from the light meter.
in S mode you choose shutter speed and the camera chooses the aperture based on ISO settings, exposure compensation settings and the reading from the light meter.
in M mode you choose either aperture or shutter speed and then adjust the other one based on the readings you get from the light meter. The reading depends on your ISO and exposure compensation settings. The reading from the light meter is normally given in the view finder in analog stule (Nikon FM3A, needle and circle) or with plus/minus signs (most of the recent cameras). Depending on the camera model, the light meter tells you in fractions of EV how much under or overexposed your current settings are.
The setting of you light meter affects the whole thing of course as well but not different as in A or S mode (or for that matter even in P mode). Exposure will be different if you use matrix, centre weight or spot meter mode.
So to come to an end, shooting in M mode adds one more thing to do to get the same result. For most of the cases it does not make sense to use M mode. You may want to use it if you want to stitch panoramic shots together from individual shots to preserve similar light conditions throughout the picture. Another application is night and low light conditions or repro work. Other than that its more of a hassel in 35mm cameras.