You have a website http://master.com and want to have a subsite http://slave.com or http://slave.master.com which is same as main site but has own menus and/or modules.

Subsite should be created as parked domain for master site in your hosting panel first.

Both master site and subsite will use same database tables and hence have same contents.

But MightySites allows you to separate menus and modules for each site. You will be able to manage each site's menus and modules from own backend panel of each site.

All other contents are managed from backend of master site as usual.

Installing/updating components and Joomla update are performed in master site only.

Each site can use own template style and load own CSS file.

All categories and all articles are same in all sites, but note that you can control display of articles for each site via menu item settings: i.e. master site can display articles from 'Master News' only and slave site from 'Slave News' only.

Note that search will display all items, custom search plugin is required to apply your logic of content separation.