Joining two domains to one WordPress

Hello guys,

I need an advice from experts as I am pretty new to WordPress and its options. I hope there will be some easy solution to my problem.

There are two websites and I want to join them together. They are both board games related, one providing written reviews nad second videos. Two different domains are merging, but we both want to keep our brand and logo, so two domains are necessary. But we want same design (only different logo) and some tweaks in design – different categories shown on main site.

These domains are now both hosted separately by different providers, none of them is running WordPress now. It would be nice to keep them separate, if possible and avoid migration of data.
But at the same time, I need same data on both instances. They would have different theme and show data differently (but it would be same data). I do not care about user rights, everything could be easily done from one WordPress, transmitting to the other.

What options to I have?
1) What can be done, when transferred under one provider?
2) Is there any way to sync WordPress instances? Would it suffice to have images on one site only as there is plenty of those?
3) Is there any other option?

Thank you for your time and help.
Dusan