And they're both called floppy disks because they use the same (general) thin magnetic film disc to store data. Some are just softer-shelled than others. That's in contrast to solid magnetic platters that were used for data storage both before and after the introduction of floppies. (and there were those huge removable, or machine-loaded mainframe style magnetic platters, too)
5 1/4" disk are 'diskettes' as well, and supposedly that's why it's spelled disk and not disc (short for diskette). I'm pretty sure 8" floppy disks were never called diskettes, but I could be wrong there too.
Though that makes me wonder if magnetic platter storage was referred to as 'disc' rather than 'disk' at some point. (obviously hard disk drives adopted the K spelling following floppies)
More to the point: the 'twist' referred to above appears to be swapping around half (or roughly so) the connections between the edge connector and pin connector portions of the cable. In mine, it's done right before connecting to the pin connector end (floppy cable runs to the edge connector, then continues before getting split into 2 chunks and swapped/overlapped before connecting up to the pin connector socket)
A single-drive cable might have one of each style connector to be universal, but cables with that twist and 2 of the same connector type or 3 or 4 connectors of mixed types would be for 2 drives.
https://www.polyplay.xyz/Connection-Cable-for … rives-FDD-cable
I swear there are some 5.25" drives around that use the newer pin block style connector, probably all 1.2MB ones, and I'm sure some of the dual 3.5+5.25" combo drives use those. (I forget if those act as single drives or can use both simultaneously, or either depending on the specific model ... some might have 2 connectors out the back, but I think they'd just need one connection with a complete pinout to support both)
And for folks new to this stuff, there's several other connectors that look superficially similar to floppy and IDE connectors, including 50-pin SCSI and a variety of proprietary or semi-proprietary CD-ROM interfaces. There may also be a reduced pin count 8-bit IDE variant of the connector, but I'm not sure about that.