This is also what's known as a collocation issue...which means we need to look at which words work best in partnership with 'think of ' and 'think about.'. Basically, 'think of' usually means 'imagine' whereas 'think about' tends to mean something closer to 'consider', so the differences would arise in certain contexts. For example, if I say I'm thinking of a tropical beach, please don't interrupt me! I mean I'm imagining it or daydreaming about it. However, a sentence like 'they're thinking about whether to agree to the sale,' means they're considering the sale. In these cases, it's just natural usage patterns that tend to favour one form over another
But when we are talking about people, we often tend to use them both in a similar way: For example, if my friend had an accident and went to hospital, I might send a card and some flowers with a message which could either read: 'I'm thinking of you,' or 'I'm thinking about you', and the meaning wouldn't be significantly different.