According to Internet Assigned Numbers Authority(IANA), three blocks of addresses are for private IP addressing, they are:

10.0.0.0/8
172.16.0.0/12 (Your IP address belongs to this group)
192.168.0.0/16

These IP addresses are usually not supported outside your LAN. This problem is usually solved by Network Address Translation (NAT) or Port Address Translation (PAT). NAT or PAT in short can be explained as a method to translate your local IP to a global IP which is recognizable outside LAN.

So what you see through ipconfig /all (172.20.192.xxx) is you local IP, which is a private IP and is not recognized in WAN (Thats why people outside NTU can not visit you);
the IP you see through FTP.SINGNET.COM.SG is "your" global IP, which is public and it is recognized in WAN. It is translated from your local IP by the router connecting outside automatically.

But NAT have its own problems: It add addtional delay; it prevents you from using peer-to-peer IP tracing tools; and it causes some problem with certain High-level Protocol/Applications.

One of the certain problem caused is PORT mode FTP transmisstion. As PORT mode use different port for control message and data, it will be stopped by NAT. Thus if your LAN is connecting outside using NAT, don't use PORT mode, use PASV mode instead.

To summary up:
1. The different address seen is caused by NAT and is nothing unnature.
2. Make sure to use PASV mode to access FTP through NAT.