One of the main differences is formality.

Speak is a little more formal than talk, and is often used in polite requests:
Example :
1. Hello, could I speak to Mr Das, please? [formal, on the telephone]
2. I’ve got a complaint: I want to speak to the manager. [formal, in a restaurant or shop]

Talk is a little less formal and is more common in spoken English:
Example :
1. What on earth are you talking about? = ‘you are not making sense’ or ‘you are not being truthful’.
2. I was talking to Ram yesterday. He told me about his new house and job.