MFM stands for Modified Frequency Modulation, also known as Delay Modulation or Miller Code. This is a self-clocking Encoding used on floppy disks of many systems including the Commodore Amiga, Atari ST and PC. It was an enhancement over FM encoding, storing roughly double the amount of “meaningful” data using the same amount of bits due its more efficient clocking, which worked by considering not just the current bit, but also the previous one.
This is why disks are marked as DD or 2D - “Double Density” since they are MFM not FM. In reality they are not really double Density by our terminology, as that would mean that the Bit Cell widths would be half the size. They are really “double storage”. The only practical difference between FM (”Single Density”) and MFM (”Double Density”) is the hardware that does the encoding and decoding, and not the disks themselves.
On the other hand, HD “High Density” disks are also MFM, but this time they do actually half the width of the bit cells to store double the amount of data. To make this storable more reliable, the disks themselves are slightly different this time in that the signal strength of the flux transitions are greater.
No wonder people got confused.
Only very old hard disks use MFM. Manufacturers went on to use more efficient encodings like RLL (Run Length Limited) and PRML (Partial Response, Maximum Likelihood). As of writing, current hard disks use an evolution of PRML called EPRML (Extended PRML).