Were external floppy drives for Atari ST and Amiga inter-compatible? For example, Commodore 1541* had its own serial bus protocol. But what about the external 3.5" DD floppy disk drive on 23pins D-Connector? I would like to have the same one to use both on Atari ST (1040STE) and on my Amigas (500+1200). And finally, what about the Amiga 1010/1011? Could I use it on Atari ST?
On both the Amiga and the Atari, external floppy drives don’t contain any “intelligence”, and the connectors are pin-to-pin. However the Amiga uses a 23-pin D connector whereas the Atari ST uses a 14-pin DIN connector, so the external drives aren’t directly compatible, and the drives themselves are setup differently.
You could build a custom cable (with circuitry) which would allow an Amiga drive to be connected to an Atari ST, or vice-versa; you’d need to account for the different expectations (that answer describes the differences between a PC floppy drive and an Amiga drive, the differences between Atari ST drives and Amiga drives are similar — see this guide for details), and you’d need to provide power to the Amiga drive. (External Amiga drives receive power through the 23-pin connector, whereas Atari ST drives have a separate power connector.)
Nowadays I would use a floppy emulator instead, or a PC floppy with an adapter. In both cases, an adapter such as this one would allow you to use the same drive with either an Amiga or an Atari (as long as you remember to configure the solder jumpers appropriately).
The Amiga and Atari ST were not compatible on either the floppy media format or on their floppy drives. The wiring is completely incompatible between the computer and the external floppy drives, most notably because the Amiga external floppy gets power from the computer and the ST external floppy has in built power supply. Also the Amiga disk format is based on 11 sectors/track, whereas the ST uses 9 sectors/track (same as PC-DOS) To my knowledge, there were no manufacturers that ever came out with an external floppy drive to support both machines. My guess would be such a device was prohibitively expensive to produce and there was not much demand.
So, then, what are the alternatives? I would say the most convenient and low-cost configuration is an internal Gotek floppy emulator for the ST. Of course, you need an ST originally equipped with an internal floppy drive. The Gotek is a direct swap, and very inexpensive. You can pursue the same solution of replacing the Amiga's internal floppy too, and all models have one.
If you want to have the freedom to move the Gotek between multiple ST or multiple Amiga machines, then just acquire an external floppy drive compatible with the machine and swap out its internal floppy mechanism for the Gotek.
Really, these Gotek devices are a super solution for both machines. The only difference between them is the firmware loaded and possibly jumper settings. And the compatibility with disk images, and ease of copying between the Gotek and real floppy disks, is basically perfect.