The way I understand it, Nintendo's engineers couldn't figure out how to design a disk system for the SNES, so they commissioned Sony to do it for them. Why would Nintendo do this if they already had this technology in the Famicom (which had a disk system)?
The two disk systems' technology were completely different.
The Famicom's disk system used a magnetic-storage floppy disk, which (according to Wikipedia) had a total capacity of 112 kilobytes (56kB per side). These were also known as Super Disks. Even when launched in 1986, this was relatively small: since 1984 IBM's PC-AT could store 1.2MB on a 5 1/4" floppy.
When Nintendo approached Sony to design a CD-based expansion for the Super Nintendo, they were looking at a medium that could hold hundreds of megabytes of data, potentially including in-game audio and video tracks. The data format developed for this add-on was confusingly known as Super Disc, but the underlying technology bore no similarity to the Famicom's add-on.
As to why Nintendo chose to work with an external company to develop a CD-based system, that is another matter entirely. It is notable that Sega developed such an add-on (known as the Sega CD or Mega-CD) in-house, and it was successfully manufactured and sold worldwide, though the games for it met with mixed reviews.