It is actually an excellent question
Basically, the DNS settings in your router are the default, as long as your clients/PCs are set to obtain IPs automatically (via DHCP). If you set DNS manually in the PC's network adapter settings, or in the web browser, you are overriding the default DNS from the router to the one you set in your browser or network adapter.
Once a name is resolved, it is remembered in local cache for a couple of hours, so that new DNS lookups are not necessary.
This also goes for Google's, or your ISP's DNS servers, they have their own cache, so that once they resolve a host from the "authoritative" server, they cache it for a while to reduce load/latency of resolving it again.
The "secure DNS" option usually is intended to bypass your ISP, and any malicious third party in the middle of your connection to a server that may attempt to log/track/hijack DNS responses.
I hope this makes sense.
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