It is very common to see JSX and React together and you'd (almost) be forgiven for thinking they were part of the same library. That is, until you came to use React and found that you had to compile any JSX before being able to run your code.
JSX is completely separate to React. Take a look: https://facebook.github.io/jsx. JSX is an ECMAscript syntax extension specification. It is intended as a declarative, Domain Specific Language (DSL) that can be compiled to Javascript.
In essence, the React JSX transpiler takes this:
<MyComponent />;