There is little difference between 'speak' and 'talk' and they are often used interchangeably.
'Speak' is often used when someone is speaking to a group of people in general. 'Speak' is also used with languages.
Peter speaks both German and Italian.
She spoke about her problems at work.
Important Note: 'Speak' tends to be used in more formal situations.
Verb Forms: Speak - Spoke - Spoken - Speaking
'Talk' is used to express informal conversation between a limited number of people.
My wife and I talked about our child's future.
She continued talking to Jack after I left the room.
Important Note:'Talk' is often used with the preposition 'about' when introducing the subject of conversation, and 'to' when introducing the conversational partner.
Verb Forms: Talk - Talked - Talked - Talking