In most cases, these two are just the same. Let’s elaborate more on what situations you should use them.
1. Making suggestions/invitations
Basically, they are just the same when it comes to making suggestions or invitations.
- How about going out tonight?
- What about going out tonight?
2. Reminder of something
“What about” is also usually used for reminding someone about something.
- A: Let’s go to the party tonight!
B: What about your exams? You should study.
I know this post doesn’t help much. However, I really think that these two are just the same and can generally be used interchangeably. So, don’t worry so much about the grammar. As long as the person you are talking to understands you, I think it’s okay. That’s what language is for anyway… communication… not the technicalities.
***Disclaimer: These are just my opinions/views on how we use these words in my country… with a little research and help from my native speaker friends. If you are a native English speaker and you see something wrong here or you want to add something, I would be very glad to hear from you. Thanks!