The Pro knows when it's running non-Pro software. As a developer with access to the PS4 devkit, there is absolutely a software difference between the two.

When running unpatched software, the PS4 Pro disables the additional compute units and underclocks its APU (which effectively underclocks the memory as well) to match the specs of the original PS4. This is why games must be patched to make use of the Pro's hardware improvements.