The Hydrogen-1 isotope is a form of hydrogen with 1 electron, 1 proton, and 0 neutrons. If that isotope were to lose its electron (thus being a Hydrogen-1 ion with a positive charge) what would be the different between it and a free proton? The positive Hydrogen-1 would contain 0 electrons, 1 proton, and 0 neutrons and the free proton would obviously contain only 1 proton. Is there a defining factor that would distinguish between a free proton and positive Hydrogen-1 ion?
The diameter of nuclei of Hydrogen atom is in the range of $1.75$ fm. You might think that, the proton lies inside this boundary in case of positive hydrogen-1 ion and the free proton doesn't have any definite boundary. It is not the case, the diameter of the nuclei of hydrogen atom is nothing but the diameter of the proton. So, there is no difference between positive hydrogen-1 ion and a free proton.