if I'm building a website for mobile the only thing that differs from desktop website is the size of the screen ? or there's additional things i have to change to be able to browse my site on mobiles ?

Yes...Mobile website URL should be registered with m.abc.com

yes but I'm using it just on my private network so no need to do this right ?

I do not understand with private network..You do not want users and search engines will see your website..

what i meant is local network I'm not gonna put it on the internet I'm gonna put it on my server so devices cpnnected to my networl can access it ?