What's the difference between "default gateway" and "preferred DNS server"?

"The default gateway is where all traffic destined for non-local networks goes to be routed to it's destination.

The preferred DNS server is the DNS server that will be used first for DNS name resolution."

"What is Default Gateway?

A default gateway is the interface address of a router and a router's job is to intercommunicate different IP networks. The default gateway works as a gateway for IP address of a network to communicate with the IP address of another IP network.

What is DNS?

DNS resolves domain name such as Google.com into IP address such as 202.22.22.22. Normally there are two types of DNS resolution, Internal DNS and External DNS. Internal DNS works for internal Domain name resolution such as if we have multiple domain entries using windows Server, windows server will resolve those entries locally as those servers are present on same network.

However when we browse the Internet, we need external DNS resolution, for which we must know that how can we reach or communicate to external DNS which is actually IP address of a different network. Now we need router to route our packet from internal network to external network for domain name resolution. Now we type IP address of DNS server so that our computer can resolve DNS requests using external IP address but as that IP address is out of our network scope, now we send our packet to router interface which is our gateway address, router routes our packet to the DNS server IP address where our DNS request gets resolved and comes back same route of default gateway.

Therefore a DNS cannot work without a Gateway address as the packet has to be routed outside our networks scope.

Without a default gateway a computer cannot reach to DNS server as DNS is an address of different network."