Tandy's TRS-80 Color Computer "CoCo" and the Dragon 32 & 64 were very similar but not clones and not the same. Floppy disk versions used totally different DOSes and disk layouts.
Both did use 18 sectors per track and 256-byte sectors though.
One of the CoCo's main disk image file format is "JVC" and is by the same guy who invented the JV1 and JV3 disk image file formats for the TRS-80 Model I and III.
Another main CoCo disk image format is "DMK", which has also been adopted in the MSX world.
The main Dragon 32 and 64 disk image file format is "VDK".
Either or both of the JV1 and JV3 formats for the TRS-80 Model I and III seem to be also used on the CoCo, but I'm never totally sure on this.
Most if not all of these formats sometimes used the generic "DSK" file extension as well as their own extension. Only "VDK" has a header with a signature.
But what I'm really not sure about is whether both platforms also use each other's image file formats. This is hard to check out when the emulators tend to support both platforms and may automatically detect what you're loading and automatically switch platform to match the file. All the CoCo and Dragon emulators seem quite tricky to use too, especially the one in MAME.
Besides system emulators there are also floppy emulators for SD cards which must have to deal with this.
For plain disks I can look for the directory structures and I can identify some boot sectors, but for nonstandard disks I'm not always sure. If I know "VDK" files are never for CoCo or "JVC" files are never for Dragon that might help.