A serial port can be many things 25 to 25, 25 to 9, or 9 to 9 with various options of male & female, DTE/DCE/Null.
The term SERIAL is actually a description of fact that data is transmitted and received over two dedicated wires one bit at a time in series as opposed to the parallel printer port that contains 8 data lines transmitting data in parallel.
The 25 pin standard was developed around early modems and many of the signal lines can be dropped thus simplifying the cable to 9 pins.
Oh yeah it wasn't mouse, it was for modem. I had one of those once. (seeming that was all you could have at the time) Mind you the mouse was 9Pin Serial too