The difference is that the Spanish tense taught in this lesson can only be used when the action is currently taking place.
For example, the english sentence "We are talking at eight tonight" could NOT be translated "Estamos hablando a las ocho esta noche" -- the action takes place in the future so the Spanish present progessive form is incorrect. But you could use "Nosotros hablamos a las ocho esta noche" since the simple present tense can look forward to near future actions.
Another example would be something like "We had a fight but we are speaking again." You couldn't use "estamos hablando" here because you are talking about "speaking" in general (you're on speaking terms again) rather than speaking at a particular moment.
In the dictionary, both to speak and to talk is translated as hablar, and I use it for both regardless of the audience. The context usually clarifies who is being addressed. Dirigir is also use when speaking of addressing an audience and perhaps is a little more specific. For to say I use decir.