"Wonder" is a verb. "Curious" is an adjective. That's the main difference. If you wonder about something, then you are probably curious about that thing. Otherwise, why would you wonder about it? If you are curious about something, then it is likely that you will sometimes wonder about it.

to wonder about something / to be curious about something - very little difference.

I agree with Jonathan's response. To add a bit more and reply to your question (Why can't I say "I wonder about Africa"?): I think that from a grammatical point of view you could construct the sentence in that way, but the problem is that the meaning might not be clear. The verb "wonder" means "want to know something", so in your first sentence it's clear that you want to know why the person came to Turkey. You can construct a sentence with the form "I wonder about NOUN/PRONOUN.", and we do a similar thing with "think" ("I think about NOUN/PRONOUN") but we generally do that where there is more context. Imagine if you said "I think about Africa." people would probably ask "In what way? What do you mean?" Why do people choose to say "I wonder about NOUN." instead of "I think about NOUN"? Often (not always!) the choice of "wonder about" expresses more doubt and perhaps suggests that the person suspects something is not quite right about the noun. So therefore it is a bit odd to hear "I wonder about Africa."