Service provider like TM has to apply to a world body for a range of IP addresses.. When Internet was created they thought will not run out but the addresses do run out. That is why now world migrates to IPv6 for more IP addresses.

So when your modem or BTU Broadband Termination Unit is case of fiber) is connected to Internet, the IP address the unit were assigned a public IP address. Then it goes to you wireless AP and the wireless AP generates private IP addresses for devices in your local LAN. The gateway for your modem or BTU is public IP address.

Therefore, when you want to connect to your house, you connect to the public IP address assigned to your home. The same was the websites you connected to www.blah-blah.com is actually a public IP address.

However, since TM have limited public IP addresses, TM has used a router at its node and the customers get private IP address on their modem (most Streamyx customers). The Unifi customer I think still get public IP address. What about service providers that use TM fiber line service. They are given even less public IP addresses. Theregore many of their end customers get private IP addresses. Those on company subscription or persons that need to have public IP address has to request and probably pay more. This is another reason company pay more.

However, there are other condition. Home user get Dynamic IP addresses though it is public IP address. Every time you connect to the service, the public IP address is assigned randomly. So, for company, they would want fixed IP address to enable anyone who access its website. If your home IP address changes all the time, you are unable to log in to your CCTV remotely.

However, there are other service that provide access even if you have dynamic IP address.

Yes, not possible with private IP address because there is no way you can type your house IP address to access your CCTV. Private IP address is just local IP address that can be the same duplicate address in other local LAN. Only public IP address unique to everyone in this world.

Another thing is that your public IP address has to be fixed. If it is randomly changed from time to time, then you are unable to know what is your IP address from remote location.

It is not with private ip but with dynamic public ip that changes. It is like what ozak mentioned. Last time, like many software, there are many free services but later become paid service.

Another way is to use an application that monitor your public IP address and send an e-mail to your private e-mail like g-mail. You can then check your e-mail for latest public IP address. However, you need to have a laptop or PC running at home 24 hours to keep mailing you. Last time there are free aplication like this but I can't recall any name.