How about is used to suggest an action. How about going shopping? How about we tidy up, and then go for a coffee? What about is used to highlight a problem or objection. What about grandma? We can't leave her on her own. I'd love to go to the beach, but what about my college work?

They both tend to have the same meaning depending on context. "How about her?" / "What about her?" is she going with us?