I don't think there's any difference. You're probably looking at similarly-designed products with different nomenclature. Based on the info you provided, I have no idea what a "USB Ethernet Card" would be insofar as it is distinct from an "Ethernet to USB Adapter".
An Ethernet to USB Adapter is a miniaturized Ethernet chipset inside an enclosure that connects to your computer's USB Host Controller. You can think of it as operating identically to having a PCI Express ethernet card mounted inside the PC chassis, except that the mechanism for communicating between the Ethernet chipset and the motherboard/CPU is USB, instead of PCIe.
If you have one computer which already has an Ethernet card installed in the chassis, and one computer that doesn't, then to connect them over Ethernet (and thus have an IP connection between them), all you need is to buy one Ethernet to USB Adapter and find or buy an Ethernet cable. Then just plug the USB male cable into the computer without an Ethernet adapter, and I think you should know how to do the rest...
I still have no idea what a USB Ethernet Card is, assuming that it is somehow distinct from what I've described above.
To the best of my knowledge, there are no products on the market that don't have "active circuitry" in the Ethernet NIC that's inline with the adapter/cable. If you were simply to map the wires between Ethernet and USB, it wouldn't work. That would be stupid. But don't be fooled by the low price of Ethernet to USB Adapters; 99.9% of them are very likely to be proper Ethernet NICs with all the accompanying circuitry; it's just that their circuitry complexity is not particularly high (especially for ones limited to 100 Mbps speeds), so you don't need a very large or expensive chip to make them.
If you manage to find someone selling adapters that just map the wires between Ethernet and USB, be sure to give their product a bad rating if they're selling it on eBay or Amazon or similar.