The cable companies need to be able to push firmware and settings to maintain the network and avoid abuse. So they have certification standards and you need to pay to play.
For example, with DOCSIS 2 modems, you could spoof the MAC address and make some config changes and get anonymous internet access at the highest service tier.
It's a completely shared infrastructure from the demarc in your home to the local cable node. It's not very secure and pretty trivial to abuse. Remember this was an infrastructure originally implemented to distribute TV signal.
Because of that TV heritage and the way they grew (on a town by town franchise basis), cable networks were usually a patchwork of really shitty networks up until fairly recently. My (limited) understanding is that on relatively modern cable systems, there is fiber connectivity to the local nodes, and then coax from that device to the homes in the area.
DSL is a switched network of sorts, and provisioning happens on the switch in the CO. Ditto for fiber.
For example, with DOCSIS 2 modems, you could spoof the MAC address and make some config changes and get anonymous internet access at the highest service tier.