grammar - What's the difference between "speak" and "talk", grammatically speaking?

There are a number of questions e.g. What is the difference between “speaking” and “talking”? and “Speak to” vs. “Speak with” that deal with the slightly different connotations of the words "speak" and "talk". However, there also seem to be some grammatical differences between the two words. This question is about whether there's a way to formally pin down these differences, or whether they're just contingent features of the two words having different histories.

Some examples of grammatical differences are as follows:

• be talkative ... be speakative


• speak French ... talk French


• give a talk ... give a speech (as opposed to a speak)


• speak up ... talk up (the meanings of the two phrases being completely different, with "up" being a preposition only in the latter case)


• speaking of which ... talking of which


• grammatically speaking ... grammatically talking

On the other hand, many other constructions work just as well with either (though they might have subtly different meanings), for example

• speak to ... talk to


• speak with ... talk with


• speak about ... talk about

I'm interested in whether there's a way to pin down these differences (e.g. are the two words classified as different types of verb in some way?), or whether they're essentially just arbitrary. I'm also interested in why we have these two different words with subtly different meanings. Is the distinction between “speak” and “talk” a feature of many languages, or is it just a peculiarity of English?

Etymologically, both words are from Germanic origins. “Talk” seems to have been formed from the Middle English tale, even though “speak” already existed in the English language by then (as far as I can tell). This makes it even more mysterious: Why did we form a new word as a synonym of one that was already established? Or were the meanings different at that time?