A static IP is a fixed IP address that is set by you, because the address is fixed if the network environment changes the IP of the device will not change. The only way for the IP to change is if you is to configure a new address.
A DHCP IP is an IP address that is configured and allocated by a DHCP Server, often this server is run as part of a router configuration and will allocate all devices on a particular network from a range of predefined addresses. DHCP allocates IP address dynamically which means that if the network environment changes, it is possible that the IP address will change with it.
If this option is selected, the IP address is randomly chosen from the Link Local Address range
169.254.0.0 to 169.254.255.255. Addresses are tested using ARP until a vacant address is identified.