Without knowing the full device models present, I can't be fully sure, but from what I can see, there isn't a difference at all between the two unplugged connectors. Both are "M-Key" m.2, which as a connector can be used for PCIe x4 SSDs as well as SATA SSDs (which one will actually work depends on the board controller, it's not guaranteed to be both).
The specific female port on the orange board will only accept m.2 SATA SSDs with the M-key notch (some are built with two notches as well), because the printing on the board suggests that it is only for SATA-based drives. PCIe NVMe SSDs will not work. It appears that the design of the board intends for the user to install the drive with the chips facing down against the white tape, instead of chips facing upwards like we usually expect when installing on a motherboard.
Now, for the black SSD plugged into a green adapter, I can't read the writing on the Samsung chip well enough to perform a proper search as to what kind of drive that is (it doesn't appear to match an mSATA notch).
It looks like if you were to flip it over an insert it, it might be too tall to fit. What drive is that?
Ahh, that's why a standard search wasn't finding it. Silly Apple proprietary connectors. That definitely makes the SSD a PCIe/NVMe model and would be incompatible with the board. There are specific adapters for those SSDs to USB that you can go with:
OWC adapter that should fit your model directly - designed for Apple's drives specifically, cost reflects that, too.
M.2 M-key NVMe adapter - This one (and others like it) may not work due to the increased height caused by the adapter board causing fitment issues, or Apple's proprietary way of doing things. But it is cheaper.