Traditionally, the AUX port is there to connect auxilliary devices. The original use case was a T1 CSU/DSU with a serial port for management. In that case, the AUX port allowed the router to provide IP address and port for telnet access.
In modern days, the AUX port server as a prot that cab provide character based or PPP based acces to ther router or external devices.
The console port is simplified with no modem or flow control but an AUX port allows flow and modem control.
For all intents and purposes, the AUX is just a flexible serial port as opposed to a restricted-use serial port (the console).
Console also has a number of special features like the ability to receive a dedlicated logging stream (logging console) and the ability to "break" into the router for diagnostics (when the BREAK function is enabled).
