Hi there!
I’m a mexican college student and I have a.. terminological doubt, I think. I’ve been lurking on this subreddit for quite a while, and found kinda strange that that what we sometimes call “Teoría de la Historia”, or theoretical history/theory of history (I think it’s what you call it) it’s often times mentioned here as philosophy of history, or the stuff that takes care of the theoretical, methodological and epistemological aspect of history. For example, the discussion around the narrative aspect of history or the epistemology of historical knowledge, or Hayden White being regarded as a “philosopher of history” instead of a theoretical, for saying something.
I know the distinction Walsh makes between speculative and critical philosophy of history, and in class we established that critical philosophy of history and theoretical history are intimately linked so... what is really the distinction between both of them?, what do you call theoretical history?, what makes the difference between those for you?, what should I read if I'm interested in theory and philosophy of history?
In the Anglophone humanities disciplines, "theory" tends to mean "critical theory" (Foucault, Derrida, Benjamin, Heidegger, etc.) whereas "philosophy" tends to designate other themes (but can include White, Hegel, what have you). Of course the critical theorists are (continental) philosophers themselves, so in principle you could lump the entire thing under "philosophy," but in practice the key difference is that someone who does "historical theory" is going to be trying to tell historical stories in light of critical theory, whereas someone talking about philosophy of history is going to be talking about history as a practice through a philosophical bent.
So Hayden White is a good example of a philosopher of history type: he's a philosopher writing about how narrative works, how historical arguments work, epistemology, etc. He's not writing work of history.
A historian who uses critical history, by contrast, is writing a work of history — a story about the past — but infusing it with the kinds of concerns of (usually French or German) philosophers. So it would be like writing a history of prisons but using Foucault not only to talk about the history, but using the history to talk about Foucault. (Foucault is a big inspiration here because he basically was trying to do something like this himself — he blended history and philosophy in making big arguments about power, sexuality, etc. Many "critical historians" would love to be thought of in this way, even if they are not Foucauldians.)
In practice this can be a loose and not always meaningful distinction, but generally speaking it "signals" the kind of work you're doing and the kind of philosophy you're interested in.