The verbs talk and speak both have the meaning ‘say words’, but they are used differently depending on context. For example speak is more formal than talk. Talk, on the other hand focuses on a speaker and at least one listener, and can mean 'have a conversation'.
We use talk for more informal situations and speak for more formal situations:
Dante will talk to the group about the benefits of meditation.
The president will speak shortly to her advisors.
We normally use to after talk and speak. We can also use with:
Could I talk to you for a moment?
The director needs to speak to you.
She spoke with the general for an hour.
I talked with her about it.
When we refer to languages, we use speak:
I don't speak Swahili, but I want to learn.
How many languages does Ahmad speak?
Some phrasal verbs require either talk or speak. Talk and speak in these contexts are not interchangeable.
His students talk back to him, because he accepts it. (talk back means to be disrespectful)
My hearing is terrible. I always need to ask people to speak up. (speak up means to speak louder)
I know we are fighting a lot now, but I want to talk it out (talk it out means to resolve problems by talking calmly)
Talk can be a noun or a verb. Speak is always only a verb.