Yes Zozo, it's the same mouse, at the backside is the a/d converter, a smd TA7533F.
I think the MB88201 is the controller chip(programmed) that changes from mouse to joystick behaviour. And could be who do the protocol, so an Amiga to MSX converter probably needs that chip, preprogrammed.....bad news.
I have an Amiga trackball connected to the internals of a striped USB Mouse(not optical). The Amiga mouses(Atari type) are very simplistic, as they give directly the movement of the disks-optocoupler pairs to the sub-d pins.
---------------------------------------------------
PS/2 to MSX!
I have a tactile surface Mouse from an old laptop PC....