the 192.168 IP is leased to your MAC address by the DHCP server running on the appartment router servicing the LAN side.( if you change your MAC address you will get a new 192.168 IP )

the appartments routers WAN side gets an address assigned to it by the ISP. it will normally change every time it reconnects.

Network address translation - Wikipedia, the free encyclopedia is done by the appartment router between the WAN and the LAN.

for most things people will see the IP address on the WAN side of the router - but skype is a slightly different issue because of the way which it performs NAT traversal , well beyond the scope of my knowledge to explain.