For all practical purposes nuclear radius and charge radius are synonymous.
Charge radius is a concept they use in their electron scattering experiments, the first of which was done under Rutherford's direction. All they did was emit helium ions at gold foil. After this experiment they knew that some central region of the atom is impenetrable. Rutherford surmised that the atomic center is the seat of an intense electric field and came up with the name Proton (literally meaning first). Since then they have measured the size of this impenetrable 'electric field' to be about 0.8775(51)*10-15 m.
But the question remains, what is it that they are measuring???? A field refers to a concept. Concepts relate objects. So what is it that causes atoms to deviate from their normal trajectory when they come close to this 'electric field'. What is a proton? What is its form? What is it comprised of? Meanwhile there is this very nebulous concept called charge. What does charge relate???
Around 1997 Gaede came up with a mercurial model and assumption of the Hydrogen atom. He supposed that the proton is a crisscrossing convergence of electric threads coming from all the atoms of the Universe. So the proton is shaped like a star. It is an intersection of electric threads. I have many pictures of the proton in previous posts on my blog. Some of these are reconstructed images of the proton done by the very scientists who use billion dollar equipment and yet do not understand what the proton in reality is.
Under Thread Theory assumption, as we approach the center of the proton electric thread density increases. The location where all the electric threads converge is impenetrable. There is a critical density of thread through which no more thread can pass. Thus when Rutherford's Helium ions came close to the gold atoms they were redirected. Essentially what happened was the tips of the magnetic threads of the Helium ions crossed paths with the critical density of electric threads of the gold atoms. A gold atom is a fusion of 79 hydrogen atoms. Thus there should be 79 impenetrable locations clustered in the center of a gold atom. For all practical purposes we can call these protons or the nucleus, but it is extremely important to note that these protons are not discrete entities. Protons are symmetrical and continuous entities. Their structure is supplied by EM Ropes coming from all atoms of the Universe. Gazillions of EM Ropes coming from all atoms of the Universe fork out to straight electric thread/axles and magnetic thread arcs. These are inseparably paired. The Magnetic Arcs oscillate as well as spin around their paired electric axle. For the motion of the magnetic arcs of the electron shell we like to use analogies such as pumping and jump roping.
Rutherford et al could not locate every single impenetrable location with their experiment. They just assumed a conceptual charge radius. The way the word 'charge' was used meant that this relates a fundamental interaction within the network of matter. Force, that is push or pull can only work with a critical density of Thread in at least one of the objects of the interaction. Thus a proton can push through thread or pull thread, usually that arced thread of an electron. It does not carry charge, rather it charges, like a horse. Horses don't carry their gallop. They gallop. Protons don't carry their charge. They charge. And they can change location by shifting along the electric axles of which they are made. This is probably what the scientists detect as nuclear spin, at least for the Hydrogen atom. As we move around the periodic table proton spin could be induced by some spinning magnetic arcs of the electron. In any case a proton can move toward or away from any atom of the Universe to which they are connected via their electric axles. They slide through EM Rope and induce it to torque.