Terminology alert!
From what I gather, the good folks over at Challenging the Common Place and Stageleft seem to think that republics are different from federations. That's unfortunately an apples and oranges comparison. The term republic refers to the type of chief of state whereas federation refers to how a state is set up administratively so it's possible to have a federation that is also a republic (such as the USA) or a federation that is also a monarchy (Canada, Australia).
So in terms of head of state there are republics and monarchies. In a republic the chief of state is a president that may or may not be elected. Generally succession is not hereditary but some form of selection process is used. Monarchies are headed by some form of monarch such as a king or queen. Succession is usually by heredity. Note that the form, republic or monarchy speaks not to how democratic the state is. Most Commonwealth monarchies are democracies where there are many totalitarian republics in the world.
The three basic ways to set up a state administratively from least powerful central government to most are confederation, federation and unitary states. Generally a confederal state has federated units (provinces, states, cantons, etc.) that are stronger vis-a-vis the central government. The central government's primary role is in defence and foreign affairs. With a federation, there are still federated units, but the power is primarily with the central government. Thus the primary difference between a confederation and federation is the amount of power wielded by the central government. This is along a continuum of course, as it is possible to have a confederal state with virtually no central government moving along until the continuum until you move into federation territory with the central government having equal power to the other end with a federation where the central government has most of the power vis-a-vis the federated units. In both cases each level of government is generally sovereign in their areas of jurisdiction. Unitary states have no federated units. A central government has all the power and makes laws for the whole country.
So my reading of both Challenging the Commonplace and Stageleft is that they are advocating in one part for a shift from a federation with a strong central government to a more confederal system where the provinces have more power vis-a-vis Ottawa. In a second part they are advocating for a shift from a monarchy to a republic. Both worthy discussions, but also separate discussions and we must be careful to use proper terminology to avoid confusion.