As a viewer you are supposed to be focused on Sarek and friends, but as a Trekkie you're supposed to notice everything from the color of the paint on the walls to the smallest costume detail.
Did you notice how strange the Tellarite ambassador's face looked? And I don't mean his pig shaped nose.
I don't know much about Tellarite anatomy, but what was the deal with the Tellarite ambassador's eyes? His eyes was so far sunken in the eye socket. It looked ridiculous. I don't know if that was intentional, or if it was just a terrible job by the make-up and costuming people. That mask was ill fitting.
It seems that the primary influence that the Federation has on its members is through the application process, where certain standards and guidelines must be met before membership can be approved.
Thus planets like Ardana can become members, but once they are members there is a limited amount of influence that can be wielded by Federation representatives on their domestic affairs.
There doesn't seem to be a one size fits all relationship between member states and the Federation.
In "Journey to Babel", Sarek told the Tellarite ambassador that he favored Coridan's admission because under Federation law, Coridan can be "protected and its wealth administered for the benefit of its people". He also mentioned that Coridan was under populated and thus unable to defend themselves. Apparently, after it becomes a member, Coridan would cede a lot of its sovereignty to the Federation. It would be dependent in a lot of ways on the Fed.
This would be in contrast to the Vulcans. From what I have seen, the Vulcans strongly guard their sovereignty and relative independence from the Feds, even though they themselves are members of the Federation. Kirk mentioned in "Amok Time" that Tpau was the only person to ever turn down a seat on the Federation Council. In the ep "Unification", it was clear that Vulcan had their own defense force.
Vulcan is to the Federation/Starfleet what France (from the 1960s to 2000s) was to NATO. They are in it, but quite independent of it at the same time.
And Earth appears to be the dominant member of the Federation, or at least of Starfleet.
Like Vulcan and Earth, each Federation member probably has developed its own term of relationship with the Federation.