I dealt with this in my recent novel
Rise of the Federation: A Choice of Futures. I needed to figure out some of the specifics of how the UFP government was organized, at least in its early years, and I used the European Union as an influence. The
European Commission is essentially the cabinet for the EU, the executive body of the government, with each member nation appointing a commissioner who's assigned to a particular portfolio and who's expected to represent the interests of the whole Union rather than their own country. So I established a Federation Commission that fills much the same role. The Federation Council is the legislature that makes the laws, and the Commission is the executive cabinet overseeing their day-to-day implementation. In this model, Hedford would've been Assistant Commissioner for Foreign Affairs or something like that.
The "High Commissioner" title for Ferris is trickier to fit into this model. In the British Commonwealth, a
High Commissioner is the senior diplomat from one member nation to another. I don't think that would've worked for Ferris, since he was called Galactic High Commissioner rather than Earth or something. Ferris's role wasn't diplomatic; he was overseeing a shipment of medical supplies, a relief mission to a member world. Also a High Commissioner was going to attend the wedding of the Dohlman of Elas, and neither Elas nor Troyius was a UFP member. An older use of the term in the British Empire was for an imperial envoy assigned to manage a protectorate, or an agent of indirect rule, while other nations have used the title for a colonial governor of sorts. I don't think that works here either.
If we went by the UN's precedent, then the High Commissioner would be the chief executive of the Federation Commission -- which would be the equivalent of the President. The problem there is that we see in the movie era and later that the UFP's chief executive is called President (and the novels have established presidents serving in the 5-year mission era and earlier). Not to mention, why would the chief executive be personally supervising a medical relief mission? That makes no sense.
Here's a thought: At the time my RotF books take place, the Federation has only a smattering of members, so each world must have several commissioners in order to fill out the total number of portfolios (cabinet posts) required. But by the 23rd century, there are dozens of members, probably more than the number of available portfolios. So maybe each department of the Commission has several commissioners, one each from various member worlds, and the High Commissioner is the senior member of that department, with the junior members being Assistant Commissioners like Hedford. Perhaps Ferris was High Commissioner for the Interior, and thus was in charge of disaster relief.