Redirect a domain

I have a site set up on the server.

I have registered another domain that I would like to point to part of the main site.

The main site is setup via Joomla and the other domain is to point to one of the menus, which is a bespoke design, just for this new domain.

I have pointed www & @ on the registrar to the server IP address.

I could setup a 301 redirect at the registrar, but I want to visitor to think that they are on a unique website, not just part of a bigger domain.

How can I achieve this?

BTW, the new domain is not set up in away on the server