The "React" part is the same regardless of web or native. But there are a lot of other concerns for web (css, DOM stuff, and integrating libraries that use those two).

Ideally web is just another taraget :) https://github.com/necolas/react-native-web

That said, while writing a website with react-native-web is potentially interesting for new sites, it can be less worthwhile for an existing site to just embed a little bit (which is one of the huge values of React). It's also still very experimental. But I suspect it will be supported in a huge way soon.