In "Journey to Babel," the Enterprise was transporting ambassadors from Federation planets to a neutral planetoid to negotiate, debate, and decide the admittance of a currently unaligned system, Coridan, to the Federation. Sarek, et al., were ambassadors from Federation planets engaged in negotiations with a non-Federation member. Calling them "ambassadors" is therefore quite the appropriate term.What does that actually mean, though? The Federation's representatives don't appear to be selected by a popular election. They called a vote to decide the issue of Coridan which came down to a vote between representatives from each government... but the representatives are AMBASSADORS, not senators or legislators.
What these ambassadors were not necessarily, though, were members of the Federation parliamentary body who represented Federation member worlds as legislators who created internal Federation law as part of the routine activity of the Federation government.
In other words, no implication of how law is created in the Federation can be gleaned from the fact that the Federation was sending ambassadors to debate and decide the issue of the admittance of Coridan to the Federation. All we know is that the power to decide that particular issue had been delegated by the Federation to the representative body of ambassadors from member worlds that the Enterprise was carrying.
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