A Series instrument will have 2 SC-1 single coil pickups, plus an HX humcancelling pickup in the middle, and the preamp adds the humcancelling signal to the pickup signals. The single coils are wound around a magnet that fills out the entire pickup shell, so the pickups are wide aperture.
The MXY is the same as an AXY, but in a shell that isn't oversized for the magnet. They are both essentailly a single coil with a humcanceller coil underneath, and the humcancelling happens within the pickup shell. They are regular aperture.
A FatBoy is an AXY with the same magnet size as an SC-1, but again with the humcancelling coil built in. This is again a wide aperture pickup. The wide aperture pickups sound a little less bright, with perhaps a bit of a low-mid boost - at least compared to AXY/MXYs.
There are a small number of MXY FatBoys out there (Mica said they were tricky to build) and they do sound different from MXYs (I have a set in an Epic).