"speak" is the common verb to express your ability to communicate. It's a very general word. "talk" and "speak" are often synonymous when referring to more specific situations e.g. I was talking / speaking to him for a long time. "talk" has a slightly more informal and relaxed feeling than "speak".

They could mean almost the same as Michael mentioned and be often interchanged . In other context they are not interchangeable as for example : He speaks German very well . You can't in that sense interchange it with 'talk' as in 'he talks German very well " 'Talk' being informal is more about conversing with someone ,exchanging ideas etc.. ,while 'speak' is relatively more concise as in expressing a message . To know exactly which to choose among both is as well a matter of usage . The more you practice you will know automatically which one is more appropriate to use in a certain context .

speak is a verb used generally about the ability to talk/speak. talk is the verb used when describing speaking/talking about specific topics or with specific people. so I speak this language, I speak with an accent. There is some overlap if you talk about topics in general e.g. I speak/talk about this topic all the time. I talk to you about problem all the time. if you say I talked to you in <language>. that would mean that in that instance you used <language> which implies that you speak it but it doesn't actually say that you have the ability to speak it.