Initial vs relative permeability

Hi,

I'm studying a toroidal core made of HP3 magnetic material. Core supplier declares its initial permeability (μi) vs frequency graph.
I made a measurement of core relative permeability (real and imaginary) and, as you can see in attached pictures, the value at low frequency is about half of supplier-declared initial permeability.

Am I correctly comparing these two parameters or aren't they the same thing?

Thanks