When Angular first came out, it handled the routing, the (two-way) data-binding, and DOM manipulation. It was the first of its kind, and it set the standards of what a client-side web application framework should look like.
Then, when React came out, it redefined what that standard is. Whilst Angular promoted its two-way data binding as a killer feature, React shunted it and called it a source of bugs; instead, it promoted one-way data-binding.
But the biggest change in the paradigm with React is the introduction of the virtual DOM and JSX.
