Be describes the state or condition of something.
Become, in contrast, means to start or to be involved in a process of change.
Today in class, my students were working on the unreal past conditional. They were trying to change history. Some wrote the following sentence, which I said was wrong. Can you see why?
If Steve Jobs hadn’t founded Apple, the iPhone would not have
I told them that they should write:
If Steve Jobs hadn’t founded Apple, the iPhone would not have become popular.
The reason is this: The iPhone is still popular now. They want to talk about something in the past–the start of iPhone’s popularity.
Here are some more descriptions of the difference between these verbs for further study: