They are often interchangeable. However speak is little more formal than talk. Also speak tends to be used in one-sided situations whereas talk suggests that two or more people are having conversation. (She spoke to her employees about the problem.) (They talked for hours about the problem.) We often use speak when saying that someone speaks in a particular way, or that we will speak to someone in order to try to get something done. (He spoke with confidence and authority.) (I’d like to speak to the manager.) When saying that someone speaks a language you only use speak! (Do you speak Chinese? NOT Do you talk Chinese?) Also there are some fixed expressions with speak and talksuch as: Speak your mind (=say what you really think) Speak up! (=raise your voice) talk sense/nonsense/rubbish talk business/sport/politics

To me there doesn't seem to be any significant difference in the meaning of those two words in most cases. On the other hand if I compare the context that these words provide when used in the following sentences there seems to be an opportunity for differentiating between those two different words; - they have been talking about the alternative ways to increase the return of their investment. - The teacher asked her to speak louder so that the pupils in the class could listen to her. Therefore, I abstractly assume that talking is in a few cases more strongly related to the logical context and the reciprocal communication which verbal expression enables where speaking seems to generally describe the use of verbal sound for communication. The difference, if existent at all is very subtle. Anyway, I wouldn't consider this etymological approach of mine a valid scientific argument if I happened to read it in a dictionary neither does such a detailed etymological analysis of words enhance the skills that an individual shall posess in a language. I suggest one should use those words in the common context that the casual use of language implies.