Is there something like a router in BuildFire that I can use to navigate between pages inside the widget?
I saw there is breadcrumbs and history.push, but it doesn't say if I have two components, how do I go between the different components.
Or should I just use the normal React Router?
There is no specific page router in BuildFire to use. You can do anything in your plugin and use any router.
You'd use Breadcrumbs to handle "Back" button navigation outside the plugin to keep the user inside the plugin.
An example would be when the user navigates within the plugin and you wish to take them back one step and not leave the plugin.