What is difference between H⁺ and proton?
There is no chemical difference, only a psychological one: how do you think about it. They are both the same thing, but many people associate $\ce{H+}$ ions with chemical reactions and protons with particle physics.
A hydrogen atom has one electron and a proton, no neutron. Therefore $\ce{H+}$ is just a proton. 

That is why acids are sometimes referred as proton donors as they donate $\ce{H+}$ to a base (also known as proton acceptor).