IP addresses are static (you pay more monthly for a static IP)
or dynamic (meaning the IP address can change when the router or modem is restarted)
The IP address is normally assigned to the router or modem, the router than assigns local IP addresses to the computers attached to the router. These IP numbers are generally 192.168.xx.xx or 10.0.x.x and are not accessible from the internet.
The router can have ports forwarded to a specific computer. Meaning when a request for a database is made, the port 5003 will forward the request to the FM Pro database on the computer that is listed in the router.