You are confusing between an EXTERNAL (PUBLIC) static IP and an internal (private) IP. When you disable DHCP, you assign INTERNAL static IPs to the various computers on your INTERNAL network. When DHCP is enabled, this job is done by the router dynamically. Neither of these options affects your public ip address.
In short, your GATEWAY (router) has your Public IP address, and the computers in your networkhave private IP Addresses. So, there is an outside and an inside. Anyone "out there" can see your public IP, but only machines inside your own network know each other's individual private IP addresses (dynamic or static).
Your ISP will charge you if you request a PUBLIC static IP. E.g., if you want to host a website or a server from your home. With a static public IP, anybody can type that into the address bar and be directed to your website. E.g. typing
http://74.125.45.100/ into your browser will take you staright to Google because that is Google's public IP.