What are dynamic and static IP addresses?

The difference lies in the validity of the addresses and how they are provided.

Static IP addresses

Static IP addresses are initially fixed and do not change. The are realized as follows:

To appear under a static address, you have to own or rent this address. This is possible with dedicated lines.
For a rented web server you can usually book a dedicated permanent IP address, when you need it.
You can assign a fixed address to each device of your own local network. They are thus independent of configuring entities such as DHCP servers and are permanently available at the same address. This can make sense in networks of manageable size. It is generally only feasible if all potential network users can be configured this way, as a duplicate IP addresses has to be avoided.

Dynamic IP addresses may change occasionally or regularly. They are often the default case.

When dialing into the Internet, the access provider assigns an IP address to you for communicating with the outside world. As the number of IP addresses is limited, you get a free address from the set of available addresses rented by your provider. Hence, the probability of a change is quite high. Dial-in access often results in another IP address with each connection. With DSL flat rates, addresses are more stable and change only occasionally. In general, providers force a disconnect every 24 hours, so there is a possibility of a change.
In order to run a Web server without a fixed IP address, you can use DNS dynamic. Here, the server appears under a stable name, and the corresponding service reflects the currently valid IP address. Of course, the service is informed of any changes to your IP address. Many routers can handle this automatically.
A rented web server is has an address assigned. If you switch servers or physical machine, it can come to change.
In a local network, all network users can have their address assigned dynamically. This is realized with the Dynamic Host Configuration Protocol. After setting up the appropriate server, all network devices are configured automatically. It is useful especially when the structure of the network or the participiants change.