As far as I know, no distinction is made between copper and tinned copper for this purpose. The bulk of the conductor is copper and the corrosion resistance and allowed connection methods are equivalent. But let's see who else chimes in.
For some specific purposes (e.g. lightning protection and Radio Frequency grounding) flat braided copper, usually tinned, is used instead of circular wire for connecting to ground electrodes, but I do not think the NEC recognizes that, since it does not correspond directly to AWG sizes.