Do I need to have a separate Squarespace site since my store has a different name?

Site URL: http://skylitlabs.co.nz

Hi. I've built my website and love it. I need to build a RELATED store-front but it has it's own domain/name and is only affiliated with my main site. I know how to put a link in the main site navigation to take people to a store but what I'm trying to figure out is since my store has a different name/domain, should I build the store SEPARATE from my current website (but also on Squarespace) and just use the link in the navigation to reach it?

OR is there a way to get rid of the navigation/header from the main site on the Store pages so that it appears to be its own entity?

Thanks.