Hi,
AUX PORT:
The purpose of the auxiliary port is for connecting to an external modem. Once configured, this modem can be used as a backup demand-dial connection to another location, or as a way to dial in to the router for troubleshooting purposes should regular connectivity fail. Unlike the console port, the auxiliary port supports hardware flow control, which ensures that the receiving device receives all data before the sending device transmits more. In cases where the receiving devices buffers become full, it can pass a message to the sender asking it to temporarily suspend transmission. This makes the auxiliary port capable of handling the higher transmission speeds of a modem.
Much like the console port, the auxiliary port is also an asynchronous serial port with an RJ-45 interface. Similarly, a rollover cable is also used for connections, using a DB-25 adapter that connects to the modem. Typically, this adapter is labeled MODEM.
VTY :
VTY stands for Virtual TeletYpe interface. It means you can connect to the daemon via the telnet protocol. A command line interface created in a router for a Telnet session. The router is able to generate a VTY dynamically.