A firewall controls and filters network traffic in and out of an environment based on security rules. Fortinet firewalls add features like VPN, IPS, web filtering, and app control to secure and segment networks.
Fortinet is the brand.
Fortigate is the firewall
Fortimanager (FMG) is a GUI, where changes are made that affects the firewall (policies, addresses, interfaces)
FortiAnalyzer (FAZ) is a GUI, where we can observe traffic that is passing the firewall. Usually your first point of contact in troubleshooting. It shows the policies hit, what happened to the traffic, and more information.