There is no such thing as a file extension name, it's a file name extension. It's called this way because file names could only be 8-byte strings initially and then this was extended with 3 extra byte places.
Neither part of the MIME type format even has to match any existing (commonly used) file name extension anyway. E.g. it can be `text/plain`. Even when it does it is just a coincidence (although very common), it actually references the format name (IIRC `image/jpeg` was used even when almost nobody were using `jpeg` for the extension and the convention was to use `jpg`).
> * file names could only be 8-byte strings initially and then this was extended*
At least part of that is not true. The ‘popular’ MS-DOS 8.3 form derives via CP/M from DEC OSes which used 6 character file names and 3 character file types, due to their use of RAD50¹ to fit 3 characters in a 16- or 18-bit word. The type field always existed, so the word ‘extension’ most likely refers to its presentation on the end of the file name, rather than an addition to a previous format.
Neither part of the MIME type format even has to match any existing (commonly used) file name extension anyway. E.g. it can be `text/plain`. Even when it does it is just a coincidence (although very common), it actually references the format name (IIRC `image/jpeg` was used even when almost nobody were using `jpeg` for the extension and the convention was to use `jpg`).