Modems connect you to the internet provider. Routers let you create your own local networks, assigning all connected devices a local IP address
Modern routers are a router, a modem, a switch and a wireless access point (AP) all combined into one. For example, that PTCL modem/router is everything just described.
Network Switches let you increase your ethernet (LAN) ports. Say your router has 4 ethernet ports, you need more, you connect a 5 port network switch and voila, you now have 7 ethernet ports total. Not 9 ports mind you, as 2 ports will be occupied for connecting the router and the switch.
Hubs are like switches, except they’re old technology and you shouldn’t buy them. They are more like splitters, as in they just forward the same network traffic to ALL outbound ports. This results in network congestion and limited speeds. Switches on the other hand analyze the incoming traffic and then decide which device it should go to.
Hubs were phased out in favor of switches.
Patch panels have ethernet ports at one end and on the other end you can punch in ethernet cables. They’re used to provide an interface to the cables. The cables can then go to different parts of your home and usually end up as a wall plate/socket where you can then connect your devices. You can just have the ethernet cables dangle around, but patch panels make the whole setup neat.
Patch panels make it easy to configure and reconfigure your network at a larger scale.