I will try to make this as simple as possible. These devices can do a ton of actions that are not listed.
Router – A router routes packets based on different metrics and algorithms. You will hear things like OSPF, EIGRP, BGP, etc.
Network firewall – This is a networking device that is used to do a few things, VPNs, network segmentation, Access-control lists, among lots of other things.
Switch – a switch works at layer 2, it creates a lot of collision domains to make collisions nearly impossible. It will also assist with vlan tagging, trunk ports, etc.
Intrusion Detection System – This is a device that inspects packets, there are different types of IDS… think SNORT or Suricata. These applications inspect the packets and will hit rules that the administrator has created. When it hits the rules, it will alert or log.
Intrusion Prevention System- same as IDS but blocks instead of alerts. This is very risky.
Load Balancers – This device has virtual servers which have Virtual IPs, behind the VIPs are pools which is a group of nodes, nodes are just servers. The request goes to the virtual server, hits the VIP, the VIP will send the request to the pool, the pool will use an algorithm to determine which serer the request goes to. Common algorithms: Round Robin, Least Connections, Weighted.