Advanced persistent threat is usually a state sponsored organization. These group carefully plan and execute their attacks and can conduct operations over a long period of time. They also have plentiful funding and only targets high value organizations.
There are numerous APTs in the world and they are either known by their APT numbers or their organizations name. APT35 aka newscaster team is an Iranian government sponsored cyber espionage team that conducts long term ISR missions. AP31 is a china nexus cyber espionage group that conducts information operations for the military. APT36 is chinese cyber group that focuses on intellectual theft and is known for their malware beacon and postsize.
APT attacks are much more complex than regular traditional web threats since they conduct manual attacks on a specific target and not an automated launch against a pool of targets. They are known to establish backdoors by using multiple backdoor shells for persistence.
To defend against APT, military has sensors all over to get full visibility across their environment as one of their protective measure. They also have cyber mission forces to conduct threat hunting missions to accompany all the cybersecurity measures already in place like firewall.