US/UK version of site with two separate landing pages?

Hi there, I have a client based in the US and UK who wants a site created with two versions; one with UK language and terminology and the other with US language and terminology.  The two site versions will have separate domain names; one for the US and one for the UK.  Do I have to create two separate sites (with 98% shared content, this is probably not advisable from an SEO point of view?), or is there a way that I can build all of this into one site and then direct the domains to two separate landing pages within the site without the user being aware of the existence of the other site version? Any advice would be much appreciated.  Many thanks 🙂