PCI-E question - connector slot

I am feeling defeated by PCI-E architecture.

I consider myself a pretty smart person but…

I have a Zimaboard with the card on the right plugged, works fine.

I bought the left card - PCI-E e-SATA to support an external Mediasonic PROBOX 4 Bay 3.5” SATA Hard Drive Enclosure via an e-SATA cable.

It doesn’t seem to be recognized ; at least, lspci is not showing it. Is this a compatible card … obviously fewer pin connectors? If not, what exactly am I looking for in terms of pin connectors. I’m quite unfamiliar with the difference in PCI-e cards when it comes to the connectors.

Not an expert

The card on the left looks to be a PCIe x1 and the card on the right look to be a PCIe X4. When I was looking into SAS cards something I keep seeing was talking of what “firmware” the cards had, this had to do with how the system could recognize the card.

There is also less bandwidth in the x1 vs X4 vs x8 (lower the number the less bandwidth it was) but that has more to do with throughput