IP address between you and your ISP can be either.
If they assign you a fixed address it should remain the same each time you log on. But if no fixed IP address is assigned then each time you log in with them it will be assigned dynamically and so be different each time.
If you have a standard router and connect to it via wireless or cable.
In this case the router gets allocated an IP address each time it connects to the internet (dynamic ip address). You can see what this is by visiting a site like whatismyip.com
You will also have an IP address on your local computer that it uses to talk to
the router. You can change the IP address range the router uses and allocates. You can find your local ip address by running a command prompt and typing ipconfig
You can also ask your internet service provider to provide you with a fixed IP address in this case your router will be allocated the same ip address each time it connects.