add on domain/subdomain

Hi, I am about to install worpress on a subdomain with an add-on domain pointing to it. I can’t seem to figure out whether when you go any deeper into the pages (e.g. a particular post page as opposed to just the index page) whether it will still show up as being under the add-on domain, or whether all the pages except the launch page will show as the subdomain?
e.g. how will worpress handle it? For instance if someone clicks ‘https://domain/wp-login.php’ (just as an example)… is it going to show them the add on domain, or the subdomain it is installed on? Or is that something that I can change on that page in WP admin. that asks you to differentiate between where you have it installed and where it ‘actually is’? (under options general, where it says WP address/blog address)
I hope that is at least vaguely clear? Essentially I am trying to keep the new ‘subdomain/add on domain’ site as separate from my major domain…. if that makes my intentions clearer?
Any ideas/help/clarification would be appreciated, thanks folks.
I can’t physically do anything yet, because my domain hasn’t propogated… I’m just trying to get a headstart on how it will all work.
Cheers,
Sam.