Most people tend to ask which is which, and majority are used to convert. How ever the proper term is in fact revert, addressing to the fact that a person is going back to what or who they once were. We are all born with the natural disposition of submitting/pleasing / serving to Allah. Somewhere along the way we just get lost and need to find our way back.
By definition conversion is a change or shift from one state or matter to another such as water to ice. Avoid tons one currency to another.
The concept in islam is based on having back to ones natural state. Before we were anything else in the world, we cane out of our mothers wounds as Muslims ( those who submit). Going back to Mother Nature, going back to Allah. Having back to your natural form of state. And may Allah guide us all to the natural state of being.