What is the difference between "speaking" and "talking"?

It seems more politically correct to say that someone is speaking rather than talking.

What is the definitive difference between these terms?

To me, it's not a matter of gentleness or political correctness. I find that speak connotes more care or intelligibility. That is, there are meaningful words and the words are clear. It could also be more formal. Since talk happens to have more uses (for example, "talk someone into" doing something, "have a talk", "give a talk", etc.), it also feels like a muddier term to me. There is the phrase "talking without saying anything", which implies idle chatter and not a lot of meaning.

So for me, speak is more formal and more precise than talk. (That applies both to the thing being described by speak or talk as well as the person using the term speak or talk.)

The two words are synonymous, but "speak" often seems to be used in a gentler way.

Compare "talk to" and "speak to"

"I will talk to him" often sounds harsher or implies the impending monologue will be harsh.

"I will speak to him" is a bit gentler, though still conveying a sense of impending correction in the coming monologue.

If you replace "to him" by "with him" in the sentences above, the message seems gentler still because "with" implies a dialogue.

_{According to NOAD:}

speak: 1 say something in order to convey information, an opinion, or a feeling. 2 talk to in order to reprove or advise.

talk: speak in order to give information or express ideas or feelings; converse or communicate by spoken words.

Obviously, the two words are synonyms. Speak can sometimes sound a little more formal than talk but there really is no "definitive difference" between the two. While there are certain contexts where I might highly favor one over the other:

Linda always speaks highly of you.

Let's talk about our vacation next year.

there are others where my preference for one over the other would be only slight:

The president will speak to reporters this afternoon.

I think you should talk with your wife, and ask her what she wants to do for Valentine's Day.

It's worth mentioning that the accompanying preposition can often change the tone of the remark. You can speak (or talk) to, speak with, speak from, speak of, speak about, or speak on. In general, talking or speaking to someone seems more one-directional, while talking or speaking with someone seems more conversational. Some of these expressions have idiomatic meaning, for example, you can speak from the heart, or you can talk about someone behind his back.

It's far too complicated to concisely say when I'd use one over the other, or when they could be used interchangeably. For example, I can think of instances where either one of these would suffice:

• I need to speak with you for a moment.
• I need to talk to you for a moment.

Those two remarks seem about “even” to me – while with seems “warmer” than to, that warmth is offset by the more formal word speak, which has the secondary meaning of “to reprove or advise.” However, there's no way to say for sure how every listener will hear and interpret such remarks.

Speaking is much more intelligible. One can speak from the heart but it would be too weird to say 'talk from the heart'. Talking is the act of saying something whilst speaking is the art of saying something.