The "classic" ones have a small adapter inside the computer case (this can be ExpressCard, a mini PCIe or an M.2 plug). They'll use either HDMI or USB 3 connect

The "classic" ones have a small adapter inside the computer case (this can be ExpressCard, a mini PCIe or an M.2 plug). They'll use either HDMI or USB 3 connectors and cabling as these can maintain reasonable signal integrity; this plugs in to the regular sized PCIe slot on the outside. There's also a barrel jack and/or a PCIe PSU connector on them for power. I don't think there's any smartness hiding inside of these, the connector and number of conductors will limit you to a ×2 or ×4 connection anyways.