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.