Application - This is a defined set of protocol and port that are used by an application.
i.e. junos-dns-udp - UDP port 53 using protocol and destination port as the main terms.
ALG - Application Layer Gateway
This is an alogorithm processing traffic that automatically performs additional functions on the firewall because the ALG recognizes the application traffic and adjusts for the expected application behavior.
i.e. FTP automatically assigns a random high port for communcations from server to client after connecting. Normally inbound internet traffic like this would be blocked by the firewall. But the FTP ALG recognizes the communications is part of the previously permitted outbound FTP connection and lets the traffic through the firewall.
ALG get associated with an application using the application-protocol term that allows it to use the ALG programming.
ALG can cause some unexpected behavior on traffic patterns. So you have the ability to turn them off globally or per policy on the SRX. The status command shows the global settings.
ALG are not connected to app-id but are a much older technology connected with standard firewall behavior.