Both display the ip address of the client. x-ClientIP is probably the same as the clientip but its configured on your device (Load Balancer or some other cloud device say WAF or CDN)
"c-ip" displays the ip address of the client. This is straight foward.
If you access weblogic server directly, it will display your PC's ip address in the log files.
However, if you access weblogic from say a load balancer, the ip address of the load balancer will get displayed in the log files. How then do you display the ip address of the client ?
Enter x-forwarded-for or x-clientIP header. This requires special configuration on the load balancer/network device. Once configured, you can display the ip address of the client using say x-clientIP even if you are accessing it using a load balancer/network device.