Firstly, without more context, it's not clear if you're talking about IP/DNS for a local network (LAN) or your Internet connection. An IP address is kind of like an identification number for your computer on a network, while the Domain Name Servers / System (DNS) could perhaps most simply be described as a phone book for that address and one that can also translate IPs into human readable forms (names and words etc.).
Every individual computer / network device will generally have a unique IP assigned to it for use on your local (home / office) network and then your ISP will also assign an IP address for the Internet connection on top that and this will be shared by all of your networked computers / devices.
In the context of the Internet connection side, a DNS usually represents the server that your ISP uses in order to translate other remote / Internet based services and IP addresses into human readable form (e.g. domain names like ISPreview.co.uk are also translated by DNS servers from an IP address). You can however change the DNS on your router to use Google's servers or OpenDNS, which may or may not improve your browsing experience vs the ISPs DNS.
Generally these are both basic network services and security considerations are largely handled at a different level (e.g. firewalls, anti-virus etc.). Take note that people on the Internet cannot see your LAN IP addresses (unless they hack into your network / computer of course), only the IP address assigned to the Internet connection by your ISP.