There is not much difference and they overlap. "Think about" emphasizes thinking about something for a while. Planning. Considering. Looking at it from different points of view. "Think of" suggests quick recall of some specific fact. "I can't think about that right now, wait until I have a little time." "What do you think about Gershwin's 'Rhapsody in Blue?'" "On the one hand, it's brilliant, I love it, and it is a landmark of U.S. musical history; on the other hand, it resembles a mere medley more than a well-structured classical piece." "You've been pretty quiet, honey, what have you been thinking about?" "Oh, our wedding plans." VERSUS "I need some more of that beer Lewis likes, but I can't think of the name." "Can you think of an ordinary English word that is eight letters long and only contains one vowel?" "On that show, when they did that dance, didn't anyone think of the children that might be watching?"

In the sense of 'consider', either can be used. In the sense of 'occur to someone', only 'think of' can be used.