No, there isn’t anything special about them from a browser’s perspective. They have been reserved so they can be re-used across private networks without conflicting with routes on the Internet. An address in the rfc1918 space isn’t magic and a shitload of corporate/campus/etc networks depend on treating them just like any other IP address when you load stuff up in a browser.

If a page loads a resource from a private address, it can easily be a local cache on the network. It can also be a dashboard like the example I gave you.

Example:

local.dashboard.example.org resolves to 192.168.255.244

dashboard.example.org resolves to some public address and web server that hosts a page that loads resources from local.dashboard.example.org