Yes, that I believe is correct. Compounded is the old fashioned traditional pestle and mortar technique, made in the back of the pharmacy in bespoke quantities to suit the individual.
Due to the nature of this, it cannot go through a regulation process as off the shelf products made in mass in a factory can.
Same active ingredient. As far as I remember, all types were known as bio-identical until NICE (perhaps?) renamed the regulated as body identical to differentiate.
As usual, assuming women do not have brain cells and need to have a more obvious name such as body. It goes along with the infantilisation of doctors now using the work poo instead of faeces, as this obviously confused us. 🙄